System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 3, Problem 3.35P
A slender rod 1.4 m long and of mass 20 kg is attached to a wheel of mass 3 kg and radius 0.05 m. as shown in Figure P3.34. A horizontal force f is applied to the wheel axle. Derive the equation of motion in terms of
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An aluminum rod of length L
=
1m has mass density p = 2700 kg and
Young's modulus E = 70 GPa. The rod is fixed at both ends. The exact
natural eigenfrequencies of the rod are wexact
E
=
√
ρ
for n=1,2,3,. . . .
1. What is the minimum number of linear elements necessary to
determine the fundamental frequency w₁ of the system? Discretize
the rod in that many elements of equal length, assemble the global
system of equations KU = w² MU, and find the fundamental
frequency w₁. Compute the relative error e₁ = (w1 - wexact) /w exact
Sketch the fundamental mode of vibration.
2. Use COMSOL to solve the same problem. Show the steps necessary
to find the fundamental frequency and mode of the rod. What is the
relative error using linear elements and a normal mesh?
A ball with a mass of 5.0 kg is hanging from a string and is initially at rest.
A bullet with a mass of 10.0 g and a velocity of 200.0 m/s is fired at the ball.
The bullet embeds itself inside the ball.
How high (h) do the ball and the bullet rise?
Gravitational acceleration: g=9.81g = 9.81g=9.81 m/s².
Don't use chatgpt.
Need handwritten solution.
Mechanical engineering
Chapter 3 Solutions
System Dynamics
Ch. 3 - Prob. 3.1PCh. 3 - A baseball is thrown horizontally from the...Ch. 3 - For the mass shown in Figure 3.1.3b. m=10 kg, =25...Ch. 3 - A particle of mass m=19 kg slides down a...Ch. 3 - A particle of mass m slides down a frictionless...Ch. 3 - A radar tracks the flight of a projectile (see...Ch. 3 - Table 3.2.1 gives the inertia IO for a point mass...Ch. 3 - A motor supplies a moment M to the pulley of...Ch. 3 - Figure P3.9 shows an inverted pendulum. Obtain the...Ch. 3 - The two masses shown in Figure P3.10 are released...
Ch. 3 - The motor in Figure P3.11 lifts the mass mL by...Ch. 3 - Instead of using the system shown in Figure 3.2.6a...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Derive the expression for the equivalent inertia...Ch. 3 - Prob. 3.18PCh. 3 - The geared system shown in Figure P3.19 represents...Ch. 3 - Prob. 3.20PCh. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - For the geared system shown in Figure P3.23,...Ch. 3 - For the geared system discussed in Problem 3.23,...Ch. 3 - The geared system shown in Figure P3.25 is similar...Ch. 3 - Consider the rack-and-pinion gear shown in Figure...Ch. 3 - The lead screw (also called a power screw or a...Ch. 3 - Prob. 3.29PCh. 3 - Derive the equation of motion of the block of mass...Ch. 3 - Assume the cylinder in Figure P3.31 rolls without...Ch. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - A slender rod 1.4 m long and of mass 20 kg is...Ch. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - The pendulum shown in Figure P3.38 consists of a...Ch. 3 - Prob. 3.39PCh. 3 - A single link of a robot arm is shown in Figure...Ch. 3 - 3.41 It is required to determine the maximum...Ch. 3 - Figure P3.42 illustrates a pendulum with a base...Ch. 3 - Figure P3.43 illustrates a pendulum with a base...Ch. 3 - 3.44 The overhead trolley shown in Figure P3.44 is...Ch. 3 - Prob. 3.45PCh. 3 - The “sky crane” shown on the text cover was a...
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