System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 4, Problem 4.12P
Calculate the expression for the natural frequency of the system shown in Figure P4.12. Disregard the pulley mass.
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Obtain the expression for the natural frequency of the system shown in
Figure P4.13. Assume small motions and disregard the pulley mass.
Figure P4.13
m
be
For 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.
Refer to Figure Q2.
A tray of mass mı is supported by 3 springs as shown in Figure 3(a). The natural frequency
fa is 5.0Hz. An additional mass motor of m2 = 3.0kg (in OFF condition) is placed at the center
on top of the mass, the natural frequency is observed to be 2.5Hz.
a) Calculate the mass mı.
The motor m2 is ON and it rotates at the speed of 600 rpm.
Calculate:
a) The transmissibility
b) Attenuation
c) Explain what will happen if the system run at Resonant Frequency
m2
m1
Figure 2(a): Original system
Figure 2(b): system with m2 added
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- For the scotch yoke mechanism shown in the figure P4.1, the horizontal position of link 4 canbe described as x = 3 cos (50t + 40°). Determine the displacement of link 4 during theinterval of 3.8 to 4.7 s.arrow_forwardA mass weighing 4 pounds is attached to a spring whose spring constant is 36 lb/ft. Find the equation of motion.arrow_forwardA simple single degree of freedom model of a wheel mounted of a spring as shown in figure below .the friction in the system is such that the wheel rolls without slipping. Calculate the natural frequency of oscillation using the energy method .Assume that no energy is lost during the contact x(t) k m,J The rotation of the wheel (of radius r) is given by 0(t) and the linear displacement is denoted by x(t). The wheel has mass ( m) and moment of inertia (J) ,and the spring has stiffness (k ).arrow_forward
- Q4 Find the transfer function for a single translational mass system with spring and damperarrow_forwardThe cylinder in the system given below is rolling withoutslip, and it is attached to the side walls with a spring and a dashpod.Find the naturan frequency, damping ratio and damped naturalfrequency of the system.arrow_forwardFor the mechanical system shown below, find the equation of motions and the system matrix. Where (x = X ewt)arrow_forward
- P4.8 Determine the rotational speed of link 3 of the mechanism given in figure P4.8 for the position shown. Use a complex numbers approacharrow_forwardQ4: - Using Laplace transforms to Find the displacement equation of mass (5 kg) attached with three elastic springs (4, 6, 2.6) N/m respectively as shown in Figure if the system vibrates from rest under critical damping. User m.arrow_forward4.76. Use modal analysis to calculate the response of the drive train system of Problem 4.44 given by the matricies to a unit impulse on the car body (i.e., at location x3). Use the modal damping of 10% in each mode. Calculate the solution in terms of physical coordinates, and after subtracting the rigid-body modes, compare the responses of each partarrow_forward
- In the pulley system shown in Figure P4.13, the input is the applied force f, and the output is the displacement x. Assume the pulley masses are negligible and derive the equation f motion. Figure P4.13 H Additionally, find the transfer function if f is the input and a is the output, and derive an expression for the natural frequency in terms of m, R, and karrow_forward2- 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_forward4.12. Figure 4.20 plots the magnitude of the steady-state oscillation of a mass sub- jected to a vibrating base. For some applications, such as an automotive suspension, the magnitude of the response is not the critical factor, but rather the net force to which the mass is subjected. 1. Determine an expression for the force to which the mass illustrated in Figure 4.18 is subjected. 2. Manipulate the expression for the force so that it is in the form of f =−khMfcos(ωt+φ). Explain the interpretation of the term Mf , which is called the force transmissi- bility. Plot Mf as a function of ω/ωn for various damping ratios to make a plot similar to Figure 4.20.arrow_forward
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