System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 4, Problem 4.30P
To determine
The Equation of motion in terms of
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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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Similar questions
- what is an air preheater, what are formulas, and their importance, define the diagram, and give me a script on how to explain the design of an air preheater, and how did values end up in that number. based on standardsarrow_forwardQf, Qa,Qm, Qcon,Qfg, Qbd, Qref,Qloss ( meaning, formula, percentage, and importance of higher value na qf, qa etc)arrow_forwardThe beam is supported by a fixed support at point C and a roller at point A. It also has an internal hinge at point B. The beam supports a point load at point D, a moment at point A and a distributed load on segment BC. a. calculate the support reactions at points A and C b. calculate the internal resultant loadings (N, V, M) at points E and F, which lies in the middle between points A and D P = 4 kip Ma = 5 kip-ft w1 = 3 kip/ft and w2 = 4 kip/ft a = 3 ftarrow_forward
- From the image of the pyramid, I want to find what s1 hat, s2 hat, and s3 hat are. I think s3 hat is just equal to e3 hat right? What about the others?arrow_forward(a) What kind of equation is it?(b) Is it linear or non-linear?(c) Is it a coupled system or uncoupled?arrow_forwardWhat kind of system is presented in Figure 2? Open loop or closed loop?arrow_forward
- What are the control hardware shown in the Figure?arrow_forwardQuestion 1. A tube rotates in the horizontal ry plane with a constant angular velocity w about the z-axis. A particle of mass m is released from a radial distance R when the tube is in the position shown. This problem is based on problem 3.2 in the text. R m 2R Figure 1 x a) Draw a free body diagram of the particle if the tube is frictionless. b) Draw a free body diagram of the particle if the coefficient of friction between the sides of the tube and the particle is = k = p. c) For the case where the tube is frictionless, what is the radial speed at which the particle leaves the tube? d) For the case where there is friction, derive a differential equation that would allow you to solve for the radius of the particle as a function of time. I'm only looking for the differential equation. DO NOT solve it. 1 e) If there is no friction, what is the angle of the tube when the particle exits? • Hint: You may need to solve a differential equation for the last part. The "potentially useful…arrow_forwardQuestion 2. A smooth uniform sphere of mass m and radius r is squeezed between two massless levers, each of length 1, which are inclined at an angle with the vertical. A mechanism at pivot point O ensures that the angles & remain the same at all times so that the sphere moves straight upward. This problem is based on Problem 3-1 in the text. P P r Figure 2 a) Draw appropriate freebody diagrams of the system assuming that there is no friction. b) Draw appropriate freebody diagrams of the system assuming that there is a coefficient of friction between the sphere and the right lever of μ. c) If a force P is applied between the ends of the levers (shown in the diagram), and there is no friction, what is the acceleration of the sphere when = 30°arrow_forward
- If you had a matrix A = [1 2 3; 4 5 6; 7 8 9] and a matrix B = [1 2 3], how would you cross multiply them i.e. what is the cross product of AxB. what would be the cross product of a dyadic with a vector?arrow_forwardProblem 3: The inertia matrix can be written in dyadic form which is particularly useful when inertia information is required in various vector bases. On the next page is a right rectangular pyramid of total mass m. Note the location of point Q. (a) Determine the inertia dyadic for the pyramid P, relative to point Q, i.e., 7%, for unit vectors ₁₁, 2, 3.arrow_forwardCan you solve for v? Also, what is A x uarrow_forward
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