System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Textbook Question
Chapter 4, Problem 4.58P
For the system shown in Figure P4.58, obtain the equation of motion in terms of
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Problem 3: The inertia matrix can be written in dyadic form which is particularly useful
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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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- A crate weighs 530 lb and is hung by three ropes attached to a steel ring at A such that the top surface is parallel to the xy plane. Point A is located at a height of h = 42 in above the top of the crate directly over the geometric center of the top surface. Use the dimensions given in the table below to determine the tension in each of the three ropes. 2013 Michael Swanbom ↑ Z C BY NC SA b x B у D Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 30 in b 43 in с 4.5 in The tension in rope AB is lb The tension in rope AC is lb The tension in rope AD is lbarrow_forwardThe airplane weighs 144100 lbs and flies at constant speed and trajectory given by 0 on the figure. The plane experiences a drag force of 73620 lbs. a.) If = 11.3°, determine the thrust and lift forces required to maintain this speed and trajectory. b.) Next consider the case where is unknown, but it is known that the lift force is equal to 7.8 times the quantity (Fthrust Fdrag). Compute the resulting trajectory angle - and the lift force in this case. Use the same values for the weight and drag forces as you used for part a. Уллу Fdrag 10. Ө Fthrust cc 10 2013 Michael Swanbom BY NC SA Flift Fweight The lift force acts in the y' direction. The weight acts in the negative y direction. The thrust and drag forces act in the positive and negative x' directions respectively. Part (a) The thrust force is equal to lbs. The lift force is equal to Part (b) The trajectory angle is equal to deg. The lift force is equal to lbs. lbs.arrow_forwardThe hoist consists of a single rope and an arrangement of frictionless pulleys as shown. If the angle 0 = 59°, determine the force that must be applied to the rope, Frope, to lift a load of 4.4 kN. The three-pulley and hook assembly at the center of the system has a mass of 22.5 kg with a center of mass that lies on the line of action of the force applied to the hook. e ΘΕ B CC 10 BY NC SA 2013 Michael Swanbom Fhook Note the figure may not be to scale. Frope = KN HO Fropearrow_forward
- Determine the tension developed in cables AB and AC and the force developed along strut AD for equilibrium of the 400-lb crate. x. 5.5 ft C 2 ft Z 2 ft D 6 ft B 4 ft A 2.5 ftarrow_forwardA block of mass m hangs from the end of bar AB that is 7.2 meters long and connected to the wall in the xz plane. The bar is supported at A by a ball joint such that it carries only a compressive force along its axis. The bar is supported at end B by cables BD and BC that connect to the xz plane at points C and D respectively with coordinates given in the figure. Cable BD is elastic and can be modeled as a linear spring with a spring constant k = 400 N/m and unstretched length of 6.34 meters. Determine the mass m, the compressive force in beam AB and the tension force in cable BC. Z D (c, 0, d) C (a, 0, b), A e B y f m BY NC SA x 2016 Eric Davishahl Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 8.1 m b 3.3 m C 2.7 m d 3.9 m e 2 m f 5.4 m The mass of the block is The compressive force in bar AB is The tension in cable S is N. kg.arrow_forwardTwo squirrels are sitting on the rope as shown. The squirrel at A has a weight of 1.2 lb. The squirrel at B found less food this season and has a weight of 0.8 lb. The angles 0 and > are equal to 50° and 60° respectively. Determine the tension force in each of the rope segments (T₁ in segment, T₂ in segment Я, and T3 in segment DD) as well as the angle a in degrees. Ө A α B Note the figure may not be to scale. T₁ = lb lb T2 T3 = = lb απ deg A BY NC SA 2013 Michael Swanbomarrow_forward
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