System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Textbook Question
Chapter 4, Problem 4.54P
Derive the equation of motion for the lever system shown in Figure P4.54, with the force f as the input and the angle
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Students have asked these similar questions
Q1: The system shown has two masses. Beam of mass (Jo#m L²
kg.m²) rotates about fixed point (O) and its free end is connected to
disk rotates about fixed point (O₂). Consider all connecting links are
massless and rigid. Find
1- The displacements of points A, B, and C in addition to the
rotations of masses, all in terms of 0.
2- Find the equation of motion (EOM) in terms of 0.
3- What is the natural frequency of the system?
0
L/2
8
Energy methods
A
Jo=m L²2
L/2
Joz-m R²
R
C
B
C
128
tion sho
4-30
4-26. Graphically position the links for the box truck,
used to load supplies onto airplanes, as shown in
Figure P4.26. Then reposition the links as the lower
sliding pin moves 0.5 m toward the cab. Determine
the resulting linear displacement of any point on the
cargo box.
actuator needs to retract.
2 m
1.5 m
1.5 m
3 m
3 m
Figure shows a mechanical system. The
connecting link has moment of inertia J about
its pivot point, and rotation angle is positive
clockwise. Position of mass m is positive to
the right. Both the angular and translational
displacements are measured from the
equilibrium position where all springs are
undeflected.
Derive the mathematical model of this system
assuming small rotation angle 8.
Link, moment.
of inertia J
L
k₁
www
m
O
k₂
www
Chapter 4 Solutions
System Dynamics
Ch. 4 - Prob. 4.1PCh. 4 - In the spring arrangement shown in Figure P4.2....Ch. 4 - In the arrangement shown in Figure P4.3, a cable...Ch. 4 - In the spring arrangement shown in Figure P4.4,...Ch. 4 - For the system shown in Figure P4.5, assume that...Ch. 4 - The two stepped solid cylinders in Figure P4.6...Ch. 4 - A table with four identical legs supports a...Ch. 4 - The beam shown in Figure P4.8 has been stiffened...Ch. 4 - Determine the equivalent spring constant of the...Ch. 4 - Compute the equivalent torsional spring constant...
Ch. 4 - Plot the spring force felt by the mass shown in...Ch. 4 - Calculate the expression for the natural frequency...Ch. 4 - Prob. 4.13PCh. 4 - Obtain the expression for the natural frequency of...Ch. 4 - 4.15 A connecting rod having a mass of 3.6 kg is...Ch. 4 - Calculate the expression for the natural frequency...Ch. 4 - For each of the systems shown in Figure P4.17, the...Ch. 4 - The mass m in Figure P4.18 is attached to a rigid...Ch. 4 - In the pulley system shown in Figure P4.19, the...Ch. 4 - Prob. 4.20PCh. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - In Figure P4.23, assume that the cylinder rolls...Ch. 4 - In Figure P4.24 when x1=x2=0 the springs are at...Ch. 4 - 4.25 In Figure P4.25 model the three shafts as...Ch. 4 - In Figure P4.26 when 1=2=0 the spring is at its...Ch. 4 - Prob. 4.27PCh. 4 - For the system shown in Figure P4.28, suppose that...Ch. 4 - For the system shown in Figure P4.29, suppose that...Ch. 4 - Prob. 4.30PCh. 4 - For Figure P4.31, the equilibrium position...Ch. 4 - Prob. 4.32PCh. 4 - Prob. 4.33PCh. 4 - 4.34 For Figure P4.34, assume that the cylinder...Ch. 4 - Use the Rayleigh method to obtain an expression...Ch. 4 - Prob. 4.36PCh. 4 - 4.37 Determine the natural frequency of the system...Ch. 4 - Determine the natural frequency of the system...Ch. 4 - Use Rayleigh's method to calculate the expression...Ch. 4 - Prob. 4.40PCh. 4 - Prob. 4.41PCh. 4 - Prob. 4.42PCh. 4 - The vibration of a motor mounted on the end of a...Ch. 4 - Prob. 4.44PCh. 4 - Prob. 4.45PCh. 4 - A certain cantilever beam vibrates at a frequency...Ch. 4 - Prob. 4.47PCh. 4 - 4.48 The static deflection of a cantilever beam is...Ch. 4 - Figure P4.49 shows a winch supported by a...Ch. 4 - Prob. 4.50PCh. 4 - Prob. 4.51PCh. 4 - Prob. 4.52PCh. 4 - 4.53 In Figure P4.53 a motor supplies a torque T...Ch. 4 - Derive the equation of motion for the lever system...Ch. 4 - Prob. 4.55PCh. 4 - Figure P4.56a shows a Houdaille damper, which is a...Ch. 4 - 4.57 Refer to Figure P4.57. Determine the...Ch. 4 - For the system shown in Figure P4.58, obtain the...Ch. 4 - Find the transfer function ZsXs for the system...Ch. 4 - Prob. 4.60PCh. 4 - Find the transfer function YsXs for the system...Ch. 4 - Prob. 4.62PCh. 4 - 4.63 In the system shown in Figure P4.63, the...Ch. 4 - Prob. 4.64PCh. 4 - Figure P4.65 shows a rack-and-pinion gear in which...Ch. 4 - Figure P4.66 shows a drive train with a spur-gear...Ch. 4 - Prob. 4.67PCh. 4 - Prob. 4.68PCh. 4 - Prob. 4.69PCh. 4 - Figure P4.70 shows a quarter-car model that...Ch. 4 - Prob. 4.71PCh. 4 - 4.72 Derive the equation of motion for the system...Ch. 4 - A boxcar moving at 1.3 m/s hits the shock absorber...Ch. 4 - For the systems shown in Figure P4.74, assume that...Ch. 4 - Refer to Figure P4.75a, which shows a ship’s...Ch. 4 - In this problem, we make all the same assumptions...Ch. 4 - Refer to Figure P4.79a, which shows a water tank...Ch. 4 - The “sky crane” shown on the text cover was a...Ch. 4 - Prob. 4.81PCh. 4 - Prob. 4.82PCh. 4 - Suppose a mass in moving with a speed 1 becomes...Ch. 4 - Consider the system shown in Figure 4.6.3. Suppose...Ch. 4 - Prob. 4.86PCh. 4 - Figure P4.87 shows a mass m with an attached...Ch. 4 - Figure P4.88 represents a drop forging process....Ch. 4 - Refer to Figure P4.89. A mass m drops from a...Ch. 4 - Prob. 4.90PCh. 4 - (a) Obtain the equations of motion of the system...Ch. 4 - Refer to part (a) of Problem 4.90. Use MATLAB to...Ch. 4 - Refer to Problem 4.91. Use MATLAB to obtain the...Ch. 4 - 4.94 (a) Obtain the equations of motion of the...Ch. 4 -
4.95 (a) Obtain the equations of motion of the...
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- Consider a pulley system shown below. Assume there is no slip between the cord and the pulley. I is the mass moment of inertia of the pulley about its own centroidal axis. Find the equations of motion in terms of x. Select all that apply.arrow_forwardP4.8 Determine the rotational speed of link 3 of the mechanism given in figure P4.8 for the position shown. Use a complex numbers approacharrow_forwardFor each of the systems shown in Figure P4.52, the input is the force f andthe outputs are the displacements x1 and x2 of the masses. The equilibriumpositions with f = 0 correspond to x1 = x2 = 0. Neglect any friction betweenthe masses and the surface. Derive the equations of motion of the systems.arrow_forward
- Question 4For the dynamic system shown in the figure,derive the equations of motion using Lagrange’s equations.arrow_forwardTwo masses A and B are 5kg and 2kg respectively rotating in a shaft. The corresponding radii of rotation are 0.2m and 0.3m respectively and the angle between the masses is 600. Find the position and magnitude of the balance mass required, if its radius of rotation is 200 mm using graphical method and also verify your answer with analytical method.arrow_forwardConsider a pulley system shown below. The coordinate x is the displacement of G. Assume there is no slip between the cord and the pulley, and disk and the ground. What is the kinetic energy of the system? Select all that apply. I don't know how to get these answers.arrow_forward
- 0.5 m, k = 500 N/m, and k = 40 N.m/rad, In the system shown, m = 10 kg, r = 0.3 m, Ko where ko is the radius of gyration of the pulley about point 0. There is no slippage between the cord and the pulley. Replace the system with an equivalent { a) torsional spring and mass moment of inertia at point 0, and b) translational mass and spring at point A. т, Ко kt А k m wwarrow_forwardA uniform rod of mass m is pivoted at a point O as shown in Figure 2. The rod is constrained by three identical linear springs, and a point mass M is attached at the end of the rod (also shown in Figure 2). The parameters of the system are as follows: L= 1 m, k = 1000 N/m, m= 50 kg, M = 25 kg. i. Derive the equation of motion of the system in terms of the angular displacement (0). Choose O as the clockwise angular displacement of the rod from the system's static equilibrium position.arrow_forwardIn the system in the figure, the static equilibrium position of the thin, slender homogeneous rod of mass m and length L is horizontal.During the movement of the system, the bar is separated from the horizontal by small angles. (A makes oscillating motion with small angles relative to the simple support point)a) Find the equation of motion of the system in terms of the given parameters.b) Since M=4 kg, m=1 kg, L=1 m, k=600 N/m, c=200 Ns/m, F=300 N, w=4 rad/s, is there resonance in the system? If there is resonance, what would you recommend to get rid of resonance?arrow_forward
- 2- Please, Derive Equation of Motion for the 2DOF system with Harmonic force due to Shaker. Note: I want EOM in Matrices form to get Natural frequencies and Mode shapes + Steady-State Response of Spring-Mass Systemarrow_forwardGiven the vibrating system below: K4 Solve for the following: K2 K1 K3 3 C4 C2 C1 C5 C3 F(t) = 200cos20t M = 10 kg K1=100 N/m K2= 80 N/m K3=75 N/m K4= 120 N/m C1 = 20Ns/m C2= 40 Ns/m C3= 35Ns/m C4= 15 Ns/m C5= 10 Ns/m 1. Damped angular velocity. 2. Type of Damping 3. Equation of motion x(t). Assume Initial conditions for displacement and velocity. 4. Graph 2 cycles of the vibrating system. You can use third party app for this. *** Show your correct and complete solution neatly in this vibration problem. ASAP! Thank you! ***arrow_forwardQuestion 9: Figure 3 shows a mechanical system. The rod (with moment of inertia J) rotates about the pivot at only small rotation angles. As pictured, theta is positive clockwise. Attached is mass m, which moves positive to the right. When stationary in the position shown, all springs are undeflected. Using BOBODDY, find the mathematical model of this system assuming small rotation angle 0. Link, moment of inertia J k3 L₁ 12 5 Ꮎ wwww Figure 3: Mechanical System m k₂ barrow_forward
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