Engineering Vibration 4th. Edition by Daniel J. Inman | 9780132871693 | 0132871696 | Holooly

Mechanical Engineering

Engineering Vibration

162 SOLVED PROBLEMS

Question: 1.9.1

Use the Euler formula to compute the numerical solution of x = -3x, x(0) = 1 for various time increments in the time interval 0 to 4, and compare the results to the exact solution. ...

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Solution First, the exact solution can be obtained...

Question: 2.3.3

As an example of using Laplace transforms to solve a homogeneous differential equation, consider the undamped single-degree-of-freedom system described by x(t) + ωn²x(t) = 0, x(0) = x0, x(0) = v0 ...

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Taking the Laplace transform of

\ddot{x}+\o...

Question: 2.3.2

Consider the system of Figure 2.12. Let J denote the inertia of the wheel and hub about the shaft, and let k denote the torsional stiffness of the system. The suspension system is subjected to a harmonic excitation as indicated. Compute an expression for the forced response using the Laplace ...

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Modeling the system as a torsional vibration probl...

Question: 2.3.1

Use the frequency response approach to compute the amplitude of the particular solution for the undamped system of equation (2.2) defined by mx(t) + kx(t) = F0 cos ωt ...

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First, write equation (2.2) with the forcing funct...

Question: 2.2.5

Derive equation (2.40) for the normalized magnitude and calculate the value of r = ω/ωn for which the amplitude of the steady-state response takes on its maximum value. ...

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From equation (2.36) the magnitude of the steady-s...

Question: 2.2.4

Consider a simple spring–mass–damper system with m = 49.2 × 10^-3 kg, c = 0.11 kg/s, and k = 857.8 N/m. Calculate the value of the steady-state response if ω = 132 rad/s for f0 = 10 N/kg. Calculate the change in amplitude if the driving frequency changes to ω = 125 rad/s. ...

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The frequency and damping ratio are determined fro...

Question: 4.1.3

Consider the matrix A defined by A = [ a b c d ] where a, b, c, and d are real numbers. Calculate values of these constants such that the matrix A is symmetric. ...

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Solution For

A

to be symmetric, [la...

Question: 4.1.2

Consider the 2 × 2 matrix K defined by K = [ k1 + k2 – k2 -k2 k2 ] (4.9) and calculate the product Kx. ...

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Again, the product is formed by considering the fi...

Question: 3.8.2

Consider again the inverted pendulum of Example 3.8.1. Design an applied force F(t) such that the response is bounded for kl < mg. ...

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The problem is to find F(t) such that θ satisfying...

Question: 3.8.1

Consider the inverted pendulum of Example 1.8.1, illustrated in Figure 3.21, and discuss its stability properties. ...

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Summing the moments about the pivot point yields [...

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