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Transient Vibrations: Chapter 7 Examples

Example 7-1

A mass, initially at rest, is subject to a step load as shown below. Determine the response of the system x(t) for t>0. Use the method of convolution.

Example 7-2

A mass, initially at rest, is subject to a ramp load as shown below. Determine the response of the system x(t) for t>0. Use the method of convolution.

Example 7-3

A mass, initially at rest, is subject to a rectangular step load as shown below. Using the the method of convolution, determine the response of the system x(t) for

  1. 0 \leq t \leq \tau,
  2. t > \tau.

Example 7-4

A mass, initially at rest, is subject to a forcing function shown below. Using the the method of convolution, determine the response of the system x(t) for

  1. 0 \leq t \leq \tau,
  2. t > \tau.

Example 7-5

A mass is initially moving such that at some time t=0 the mass has position x_0 and velocity v_0. At that instant a step load is applied to the mass as shown below.
Determine the response of the system x(t) for t>0 using

  1. Newton’s laws directly,
  2. The method of convolution.

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