# (Solved) : Physics Classical Dynamics Of Particles0b08 . . .

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1 Million+ Step-by-step solutions Q:For the systems shown in Figure, assume that the resultingFor the systems shown in Figure, assume that the resulting motion is small enough to be only horizontal and determine the expression for the equivalent damping coefficient ce that relates the applied force f to the resulting velocity v.
a.

b.

Q:Refer to Figure a, which shows a ship’s propeller, driveRefer to Figure a, which shows a ship’s propeller, drive train, engine, and flywheel. The diameter ratio of the gears is D1/D2 = 1.5. The inertias in kg-m2 of gear 1 and gear 2 are 500 and 100, respectively. The flywheel, engine, and propeller inertias are 104, 103, and 2500, respectively. The torsional stiffness of shaft 1 is 5 x 106 N-m/rad, and that of shaft 2 is 106 N-m/rad. Because the flywheel inertia is so much larger than the other inertias, a simpler model of the shaft vibrations can be obtained by assuming the flywheel does not rotate. In addition, because the shaft between the engine and gears is short, we will assume that it is very stiff compared to the other shafts. If we also disregard the shaft inertias, the resulting model consists of two inertias, one obtained by lumping the engine and gear inertias, and one for the propeller (Figure b). Using these assumptions, obtain the natural frequencies of the system.
a.

b.

Q:In this problem, we make all the same assumptions asIn this problem, we make all the same assumptions as in Problem 4.75, but we do not discount the flywheel inertia, so our model consists of three inertias, as shown in Figure. Obtain the natural frequencies of the system.
Q:Refer to Figure, which shows a turbine driving an electricalRefer to Figure, which shows a turbine driving an electrical generator through a gear pair. The diameter ratio of the gears is D2/D1 = 1.5. The inertias in kg-m2 of gear 1 and gear 2 are 100 and 500, respectively. The turbine and generator inertias are 2000 and 1000, respectively. The torsion stiffness of shaft 1 is 3 x 105 N-m/rad, and that of shaft 2 is 8 x 104 N-m/rad. Disregard the shaft inertias and obtain the natural frequencies of the system.
Q:Refer to Figure, which is a simplified representation of aRefer to Figure, which is a simplified representation of a vehicle striking a bump. The vertical displacement x is 0 when the tire first meets the bump. Assuming that the vehicle’s horizontal speed v remains constant and that the system is critically damped, obtain the expression for x(t).
Q:Refer to Figure a, which shows a water tank subjectedRefer to Figure a, which shows a water tank subjected to a blast force f(t). We will model the tank and it’s supporting columns as the mass-spring system shown in part (b) of the figure. The blast force as a function of time is shown in part (c) of the figure. Assuming zero initial conditions, obtain the expression for x(t).
a.

b.

c.

Q:The beam shown in Figure has been stiffened by theThe beam shown in Figure has been stiffened by the addition of a spring support. The steel beam is 3 ft long, 1 in thick, and 1 ft wide, and its mass is 3.8 slugs. The mass m is 40 slugs. Neglecting the mass of the beam,
a. Compute the spring constant k necessary to reduce the static deflection to one-half its original value before the spring k was added.
b. Compute the natural frequency con of the combined system.
Q:The “sky crane” shown on the text cover was aThe “sky crane” shown on the text cover was a novel solution to the problem of landing the 2000 lb Curiosity rover on the surface of Mars. Curiosity hangs from the descent stage by 60-ft long nylon tethers (Figure a). The descent stage uses its thrusters to hover as the rover is lowered to the surface. Thus the rover behaves like a pendulum whose base is moving horizontally. The side thruster force is not constant but is controlled to keep the descent stage from deviating left or right from the desired vertical path. As we will see in Chapter 10, such a control system effectively acts like a spring and a damper, as shown in Figure b. The rover mass is mr. the descent stage mass is md, and the net horizontal component of the thruster forces is f = kx + e. Among other simplifications, this model neglects vertical motion and any rotational motion. Derive the equations of motion of the system in terms of the angle θ and the displacement x.
a.

b.

Q:Obtain the equations of motion for the system shown inObtain the equations of motion for the system shown in Figure for the case where m1 = m2 and m2 = 2m. The cylinder is solid and rolls without slipping. The platform translates without friction on the horizontal surface.
Q:Obtain the equations of motion for the system shown inObtain the equations of motion for the system shown in Figure for the case where m1 = m2 = m. The cylinder is solid and rolls without slipping. The platform translates without friction on the horizontal surface.
Q:In Figure a tractor and a trailer is used toIn Figure a tractor and a trailer is used to carry objects, such as a large paper roll or pipes. Assuming the cylindrical load m3 rolls without slipping, obtain the equations of motion of the system.
Q:Suppose a mass m moving with a speed v1 becomesSuppose a mass m moving with a speed v1 becomes embedded in mass m2 after striking it (Figure 4.6.1). Suppose m2 = 5m. Determine the expression for the displacement x(t) after the collision.
Q:Consider the system shown in Figure 4.6.3. Suppose that theConsider the system shown in Figure 4.6.3. Suppose that the mass m moving with a speed v rebounds from the mass m2 = 5m after striking it. Assume that the collision is perfectly elastic. Determine the expression for the displacement x(t) after the collision.
Q:The mass m1 is dropped from rest a distance hThe mass m1 is dropped from rest a distance h onto the mass m2, which is initially resting on the spring support (Figure). Assume that the impact is inelastic so that mi sticks to m2. Calculate the maximum spring deflection caused by the impact. The given values are m1 = 0.5 kg, m2 = 4 kg,
k = 400 N/m, and h = 2m.
Q:Figure shows a mass m with an attached stiffness, suchFigure shows a mass m with an attached stiffness, such as that due to protective packaging. The mass drops a distance h, at which time the stiffness element contacts the ground. Let x denote the displacement of m after contact with the ground. Determine the maximum required stiffness of the packaging if a 10 kg package cannot experience a deceleration greater than 8g when dropped from a height of 2 m.
Q:Figure represents a drop forging process. The anvil mass isFigure represents a drop forging process. The anvil mass is m1 = 1000 kg, and the hammer mass is m2 = 200 kg. The support stiffness is k = 107 N/m, and the damping constant is c = 1 N-s/m. The anvil is at rest when the hammer is dropped from a height of h= 1 m. Obtain the expression for the displacement of the anvil as a function of time after the impact. Do this for two types of collisions:
(a) An inelastic collision
(b) A perfectly elastic collision.
Q:Refer to Figure. A mass m drops from a heightRefer to Figure. A mass m drops from a height h and hits and sticks to a simply supported beam of equal mass. Obtain an expression for the maximum deflection of the center of the beam. Your answer should be a function of h, g, m, and the beam stiffness k.
Q:Determine the equivalent spring constant of the arrangement shown inDetermine the equivalent spring constant of the arrangement shown in Figure. All the springs have the same spring constant k.
Q:(a) Obtain the equations of motion of the system shown(a) Obtain the equations of motion of the system shown in Figure. The masses are m1 = 20 kg and m2 = 60 kg. The spring constants are k1 = 3 x 104 N/m and k2 = 6 x 104 N/m.
(b) Obtain the transfer functions X1(s)/F(s) and X2(s)/F(s).
(c) Obtain a plot of the unit-step response of x1 for zero initial conditions.
Q:(a) Obtain the equations of motion of the system shown(a) Obtain the equations of motion of the system shown in Figure.
(b) Suppose the inertias are I1 = I and I2 = 21 and the torsional spring constants are k1 = k2 = h = k. Obtain the transfer functions Æ1(s)/T2(s) and Æ2(s) / T2(s) in terms of I and k.
(c) Suppose that I = 10 and k = 60. Obtain a plot of the unit-impulse response of Î¸ for zero initial conditions.
Q:Refer to part (a) of Problem 4.90. Use MATLAB toRefer to part (a) of Problem 4.90. Use MATLAB to obtain the transfer functions X1(s)/F(s) and X2(s)/F(s). Compare your answers with those found in part (b) of Problem 4.90.
In Question 90
(a) Obtain the equations of motion of the system shown in Figure. The masses are m1 = 20 kg and m2 = 60 kg. The spring constants are k1 =3 x 104 N/m and k2 = 6 x 104 N/m.
(b) Obtain the transfer functions X1(s)/F(s) and X2(s)/F(s).
Q:Refer to Problem 4.91. Use MATLAB to obtain the transferRefer to Problem 4.91. Use MATLAB to obtain the transfer functions Ɵ1(s)/T2(s) and Ɵ2(s)/T2(s) for the values I1 = 10, I2 = 20, and k1 = k2 = k3 = 60. Compare your answers with those found in part (b) of Problem 4.91.
In Problem 91
Suppose the inertias are I1 = I and I2 = 21 and the torsional spring constants are k1 = k2 = h = k. Obtain the transfer functions Ɵ1(s)/T2(s) and Ɵ2(s) / T2(s) in terms of I and k.
Q:(a) Obtain the equations of motion of the system shown(a) Obtain the equations of motion of the system shown in Figure. Assume small angles. The spring is at its free length when Î¸1 = Î¸2 = 0.
(b) For the values m1 = 1 kg, m2 = 4 kg, k = 10 N/m, L1 = 2 m, and L2 = 5 m, use MATLAB to plot the free response of Î¸1 if Î¸1(0) = 0.1 rad and Î¸1 (0) = Î¸2 (0) = Î¸2 (0) = 0.
Q:(a) Obtain the equations of motion of the system shown(a) Obtain the equations of motion of the system shown in Figure.
(b) Suppose that the masses are m1 = 1 kg, m2 = 2 kg, and the spring constants are k1 = k2 = k3 = 1.6 x 104 N/m. Use MATLAB to obtain the plot of the free response of x1. Use x1 (0) = 0.1 m, x2(0) = 1 (0) = 2(0) = 0.
Q:Obtain the transfer function X(s)/F(s) from the block diagram shownObtain the transfer function X(s)/F(s) from the block diagram shown in Figure.
Q:Use the MATLAB series and feedback functions to obtain theUse the MATLAB series and feedback functions to obtain the transfer functions C(s)/R(s) and C(s)/D(s) for the block diagram shown in Figure.
Q:Obtain the state model for the reduced-form model 5 +Obtain the state model for the reduced-form model 5 + 7 + 4x = f(t).
Q:Obtain the state model for the reduced-form model 2 d3y/dt3 +Obtain the state model for the reduced-form model
2 d3y/dt3 + 5 d2y/dt2 + 4dy/dt + 7y = f(t)
Q:Obtain the state model for the reduced-form model 2 +Obtain the state model for the reduced-form model 2 + 5 + 4x = 4y(t).
Q:Obtain the state model for the transfer-function model Y(s)/F(s) = 6/(3s2Obtain the state model for the transfer-function model
Y(s)/F(s) = 6/(3s2 + 6s + 10)
Q:Obtain the state model for the two-mass system whose equationsObtain the state model for the two-mass system whose equations of motion are
m1(1 + k1(x1 – x2) = f(t)
m22 – k1(x1 – x2) + k2x2 = 0
Q:Obtain the state model for the two-mass system whose equationsObtain the state model for the two-mass system whose equations of motion for specific values of the spring and damping constants are
101 + 81 – 52 + 40×1 – 25×2 = 0
52 – 25×1 + 25×2 -5×1+52 = f(t)
Q:Put the following model in standard state-variable form and obtainPut the following model in standard state-variable form and obtain the expressions for the matrices A, B, C, and D. The output is x.
2 + 5 + 4x = 4y(t)
Q:Given the state-variable model 1 = – 5×1 + 3×2 +Given the state-variable model
1 = – 5×1 + 3×2 + 2u1
2 = – 4×2 + 6u2
and the output equations
y1=x1 + 3×2 + 2u1
y2 = x2
Q:Given the following state-variable models, obtain the expressions for theGiven the following state-variable models, obtain the expressions for the matrices A, B, C, and D for the given inputs and outputs.
a. The outputs are x1 and x2; the input is u.
1 = – 5×1 + 3×2
2 = x1 – 4×2 + 5u
b. The output is x1; the inputs are u1 and u2.
1 = -5×1 + 3×2 + 4u1
2 = x1 – 4×2 + 5u2
Q:Obtain the transfer function X(s)/F(s) from the block diagram shownObtain the transfer function X(s)/F(s) from the block diagram shown in Figure.
Q:Obtain the expressions for the matrices A, B, C, andObtain the expressions for the matrices A, B, C, and D for the state-variable model you obtained in Problem 16. The outputs are xi and x2.
In Problem 16
101 + 81 – 52 + 40×1 – 25×2 = 0
52 – 25×1 + 25×2 -5×1+52 = f(t)
Q:The transfer function of a certain system is Y(s)/F(s) = (6sThe transfer function of a certain system is
Y(s)/F(s) = (6s + 7)/(s + 3)
Use two methods to obtain a state-variable model in standard form. For each model, relate the initial value of the state-variable to the given initial value y(0).
Q:The transfer function of a certain system is Y(s)/ F(s) =The transfer function of a certain system is
Y(s)/ F(s) = (s + 2)/(s2 + 4s + 3)
Use two methods to obtain a state-variable model in standard form. For each model, relate the initial values of the state variables to the given initial values y(0) and (0).
Q:Use MATLAB to create a state-variable model; obtain the expressionsUse MATLAB to create a state-variable model; obtain the expressions for the matrices A, B, C, and D, and then find the transfer functions of the following models, for the given inputs and outputs.
a. The outputs are x1 and x2; the input is u.
1 = -5×1 + 3×2
2 = x1 – 4×2 + 5u
b. The output is xi; the inputs are u1 and u2.
1 = -5×1 + 3×2 + 4u1
2 = x1 – 4×2 + 5u2
Q:Use MATLAB to obtain a state model for the followingUse MATLAB to obtain a state model for the following equations; obtain the expressions for the matrices A, B. C. and D. In both cases, the input is f(t); the output is y.
a.

b.
Y(s)/F(s) = 6/(3s2+ 6s + 10)

Q:Use MATLAB to obtain a state-variable model for the followingUse MATLAB to obtain a state-variable model for the following transfer functions, a.
a.
Y(s)/F(s) = (6s + 7)/(s + 3)
b.
Y(s)/ F(s) = (s + 2)/(s2 + 4s + 3)
Q:For the following model the output is x1 and theFor the following model the output is x1 and the input is f(t).
1 = – 5×1 + 3×2
2 = x1 – 4×2 + 5f(t)
a. Use MATLAB to compute and plot the free response for x1 (0) = 3, and x2(0) = 5.
b. Use MATLAB to compute and plot the unit-step response for zero initial conditions.
c. Use MATLAB to compute and plot the response for zero initial conditions with the input f(t) = 3sin 10πt, for 0 ≤ / ≤ 2.
d. Use MATLAB to compute and plot the total response using the initial conditions given in Part (a) and the forcing function given in part (c).
Q:Given the state-variable model x1 = -5×1 + 3×2 + 2u1 x2Given the state-variable model
x1 = -5×1 + 3×2 + 2u1
x2 = -4×2 + 6u2
And the output equations
y1 = x1 + 3×2 + 2u1
y2 = x2
Use MATLAB to find the characteristic polynomial and the characteristic roots.
Q:The equations of motion for a two-mass, quarter-car model ofThe equations of motion for a two-mass, quarter-car model of a suspension s stem are
m11 = c1(2 -1) +k1(x2 -x1)
m22 = -c1(2 – 1) – k1(x2 – x1) + k2(y – x2)
Suppose the coefficient values are: m1 = 240 kg, m2 = 36 kg, k1 = 1.6 x 104 N/m, k2 = 1.6 x 105 N/m, c1 = 98 N .s/m.
a. Use MATLAB to create a state model. The input is y(t); the outputs are x1 and x2.
b. Use MATLAB to compute and plot the response of x1 and x2 if the input y(t) is a unit impulse and the initial conditions are zero.
c. Use MATLAB to find the characteristic polynomial and the characteristic roots.
d. Use MATLAB to obtain the transfer functions X1(s)/Y(s) and X2(s)/Y(s).
Q:A representation of a car’s suspension suitable for modeling theA representation of a car’s suspension suitable for modeling the bounce and pitch motions is shown in Figure, which is a side view of the vehicle’s body showing the front and rear suspensions. Assume that the car’s motion is constrained to a vertical translation x of the mass center and rotation θ about a single axis which is perpendicular to the page. The body’s mass is m and its moment of inertia about the mass center is IG. As usual, x and θ are the displacements from the equilibrium position corresponding to y1 = y2 = 0. The displacements y1 (t) and y2(t) can be found knowing the vehicle’s speed and the road surface profile.
a. Assume that x and θ are small, and derive the equations of motion for the bounce motion x and pitch motion θ.
b. For the values k1 = 1100 lb/ft, k2 = 1525 lb/ft. c1 = c2 = 4 lb-sec/ft, L1, = 4.8 ft, L2 = 3.6 ft, m = 50 slugs, and IG = 1000 slug-ft2, use MATLAB to obtain a state-variable model in standard form.
Q:Obtain the transfer function X(s)/F(s) from the block diagram shownObtain the transfer function X(s)/F(s) from the block diagram shown in Figure.
Q:A. Use a MATLAB ode function to solve the followinga. Use a MATLAB ode function to solve the following equation for 0 ≤ / ≤ 12. Plot the solution.
= cost
y(0) = 6
b. Use the closed-form solution to check the accuracy of the numerical method.
Q:A. Use a MATLAB ode function to solve the followinga. Use a MATLAB ode function to solve the following equation for 0 ≤ / ≤ 1. Plot the solution.
= 5e-4t
y(0) = 2
b. Use the closed-form solution to check the accuracy of the numerical method.
Q:A. Use a MATLAB ode function to solve the followinga. Use a MATLAB ode function to solve the following equation for 0 ≤ t ≤ l. Plot the solution.
+ 3y = 5e4t
y(0) = 10
b. Use the closed-form solution to check the accuracy of the numerical method.
Q:A. Use a MATLAB ode function to solve the followinga. Use a MATLAB ode function to solve the following nonlinear equation for 0 ≤ t ≤ 4. Plot the solution.
+ sin y = 0
y(0) = 0.1
b. For small angles, sin y ( y. Use this fact to obtain a linear equation that approximates equation (1). Use the closed-form solution of this linear equation to check the output of your program.
Q:Sometimes it is tedious to obtain a solution of aSometimes it is tedious to obtain a solution of a linear equation, especially if all we need is a plot of the solution. In such cases, a numerical method might be preferred. Use a MATLAB ode function to solve the following equation for 0 ≤ t ≤ 7. Plot the solution.
y + 2y = f(t)
y(0) = 2
Where

Q:A certain jet-powered ground vehicle is subjected to a nonlinearA certain jet-powered ground vehicle is subjected to a nonlinear drag force. Its equation of motion, in British units, is
50 = f – (20u + 0.05u2)
Use a numerical method to solve for and plot the vehicle’s speed as a function of time if the jet’s force is constant at 8000 lb and the vehicle starts from rest.
Q:The following model describes a mass supported by a nonlinear,The following model describes a mass supported by a nonlinear, hardening spring. The units are SI. Use g = 9.81 m/s2.
5 = 5g – (900y+ 1700y3)
Q:Van der Pol’s equation is a nonlinear model for someVan der Pol’s equation is a nonlinear model for some oscillatory processes. It is
-b(1 – y2) + y = 0
Q:Van der Pol’s equation is -b(1- y2) + y =Van der Pol’s equation is
-b(1- y2) + y = ()
This equation can be difficult to solve for large values of the parameter b. Use b = 1000 and 0 ≤ f ≤ 3000, with the initial conditions y(0) = 2 and (0) = 0. Use ode45 to plot the response.
Q:The equation of motion for a pendulum whose base isThe equation of motion for a pendulum whose base is accelerating horizontally with an acceleration a(t) is
Lθ + g sin θ = a(t)cosθ
Suppose that g = 9.81 m/s2, L = 1 m, and θ (0) = 0. Solve for and plot θ (f) for 0 ≤ / ≤ 10 s for the following three cases.
a. The acceleration is constant: a = 5 m/s2, and θ (0) = 0.5 rad.
b. The acceleration is constant: a = 5 m/s2, and θ (0) = 3 rad.
c. The acceleration is linear with time: a = 0.5t m/s2, and θ (0) = 3 rad.
Q:Draw a block diagram for the following equation. The outputDraw a block diagram for the following equation. The output is X(s) the inputs are F(s) and G(s).
5 + 3+ 7x = 10/(0 – 4g(f)
Q:Suppose the spring in Figure is nonlinear and is describedSuppose the spring in Figure is nonlinear and is described by the cubic force-displacement relation. The equation of motion is
m = c( – ) + k1(y – x) + k2(y – x)3
Where m = 100, c = 600, k1 = 8000, and k2 = 24000. Approximate the unit-step input y(t) with y(t) = 1 – e-t/Ï, where r is chosen to be small compared to the period and time constant of the model when the cubic term is neglected. Use MATLAB to plot the forced response x(t).
Q:Create a Simulink model to plot the solution of theCreate a Simulink model to plot the solution of the following equation for 0 ≤ t ≤ 6.
10 = 7 sin 4t + 5 cos 3t
y (0) = 4
(0) = I
Q:A projectile is launched with a velocity of 100 m/sA projectile is launched with a velocity of 100 m/s at an angle of 30° above the horizontal. Create a Simulink model to solve the projectile’s equations of motion, where x and y are the horizontal and vertical displacements of the projectile.
= 0
x(0) = 0
(0) = 100 cos 30°
= -g
y(0) = 0
(0) = 100 sin 30°
Use the model to plot the projectile’s trajectory y versus x for 0 ≤ f ≤ 10 s.
Q:In Chapter 2 we obtained an approximate solution of theIn Chapter 2 we obtained an approximate solution of the following problem, which has no analytical solution even though it is linear.
+x = tan t………………. x(0) = 0
The approximate solution, which is less accurate for large values of t, is
x(t) = 1/3 t3 -r2 + 3t -3 + 3e-t
Create a Simulink model to solve this problem and compare its solution with the approximate solution over the range 0 ≤ t ≤ l
Q:Construct a Simulink model to plot the solution of theConstruct a Simulink model to plot the solution of the following equation for 0 15 + 5x = Aus, (t) – 4us (t – 2)……………………x(0) = 2
Q:Use Simulink to solve Problem 18 for zero initial conditions,Use Simulink to solve Problem 18 for zero initial conditions, u1 a unit-step input, and u2: = 0.
In Problem 18
Given the state-variable model
1 = – 5×1 + 3×2 + 2u1
2 = – 4×2 + 6u2
and the output equations
y1=x1 + 3×2 + 2u1
y2 = x2
Q:Use Simulink to solve Problem 18 for the initial conditionsUse Simulink to solve Problem 18 for the initial conditions x1(0) = 4, x2(0) = 3, and u1 = u2 = 0.
In problem 18
Given the state-variable model
1 = – 5×1 + 3×2 + 2u1
2 = – 4×2 + 6u2
and the output equations
y1=x1 + 3×2 + 2u1
y2 = x2
Q:Use Simulink to solve Problem 19a for zero initial conditionsUse Simulink to solve Problem 19a for zero initial conditions and u = 3 sin 2t.
In Problem 19a
The outputs are x1 and x2; the input is u.
1 = – 5×1 + 3×2
2 = x1 – 4×2 + 5u
Q:Use Simulink to solve Problem 26c. In Problem 26c Use MATLAB toUse Simulink to solve Problem 26c.
In Problem 26c
Use MATLAB to compute and plot the response for zero initial conditions with the input f(t) = 3sin 10πt, for 0 ≤ / ≤ 2.
Q:Use the Transfer Function block to construct a Simulink modelUse the Transfer Function block to construct a Simulink model to plot the solution of the following equation for 0 ≤ t ≤ 4.
2 + I2 + 10×2 = 5us(t) – 5us(t – 2)
x(0) = (0) = 0
Q:Draw a block diagram for the following model. The outputDraw a block diagram for the following model. The output is X(s) the inputs are F(s) and G(.v). Indicate the location of Y(s) on the diagram.
= y – 5x + g(t)
= I0f(t) – 30x
Q:Construct a Simulink model to plot the solution of theConstruct a Simulink model to plot the solution of the following equation for 0 ≤ t ≤ 4.
2 + 12 + 10×2 = 5 sin 0.8t
x(0) = (0) = 0
Q:Use the Saturation block to create a Simulink model toUse the Saturation block to create a Simulink model to plot the solution of the following equation for 0 ≤ t ≤ 6.
3 + y = f(t)
y(0) = 2
Where

Q:Construct a Simulink model of the following problem. 5 + sinConstruct a Simulink model of the following problem.
5 + sin x = f(t)
x(0) = 0
The forcing function is
Q:Create a Simulink model to plot the solution of theCreate a Simulink model to plot the solution of the following equation for 0 ≤ t ≤ 3.
+ 10×2 = 2 sin 4t
x(0) = 1
Q:Construct a Simulink model of the following problem. 10 + sinConstruct a Simulink model of the following problem.
10 + sin x = f(t)
x(0) = 0
The forcing function is f(t) = sin 2t. The system has the dead-zone nonlinearity shown in Figure 5.6.6.
Q:The following model describes a mass supported by a nonlinear,The following model describes a mass supported by a nonlinear, hardening spring. The units are SI. Use g = 9.81 m/s2.
5 = 5g – (900y + 1700y3)
y(0) = 0.5
(0) = 0.
Q:Consider the system for lifting a mast, discussed in ChapterConsider the system for lifting a mast, discussed in Chapter 3 and shown again in Figure. The 70-ft-long mast weighs 500 lb. The winch applies a force f = 380 lb to the cable. The mast is supported initially at an angle of Î¸ = 30Â° and the cable at A is initially horizontal. The equation of motion of the mast is
25,400Î¸ = -17,500 cos Î¸ + 626000/Q sin(1.33 + Î¸)
Where
Q = â(2020+ 1650 cos (l .33 + Î¸)) Create and run a Simulink model to solve for and plot Î¸ (t) for Î¸ (t) â¤ Ï/2 rad.
Q:A certain mass, m = 2 kg, moves on aA certain mass, m = 2 kg, moves on a surface inclined at an angle ( = 30° above the horizontal. Its initial velocity is v(0) = 3 m/s up the incline. An external force of f1 = 5 N acts on it parallel to and up the incline. The coefficient of dynamic friction is μd = 0.5. Use the Coulomb Friction block or the Sign block and create a Simulink model to solve for the velocity of the mass until the mass comes to rest. Use the model to determine the time at which the mass comes to rest.
Q:If a mass-spring system has Coulomb friction on the horizontalIf a mass-spring system has Coulomb friction on the horizontal surface rather than viscous friction, its equation of motion is
m = -ky +f/(t) – μmg if > 0
m = – ky + f(t) + μmg if Where μ is the coefficient of friction develop a Simulink model for the case where m = 1 kg, k = 5 N/m, μ = 0.4, and g = 9.8 m/s2. Run the simulation for two cases:
(a) The applied force f(t) is a step function with a magnitude of 10 N,

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