3.19 by Paul is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

# 3.19

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3.19 by Paul is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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I think the natural frequency is actually sqrt(10)

Based on what is written on this page you are right! However, I mis-copied the problem from the textbook. The value for was given by the problem as 75 kN/m. Sorry about that.

Why is weight, mg, not included in the FBD?

Problems like this one are interested only in the steady state operation of the system. This means that we are going to let the system's motion play out for a long time before we start looking at it; based on this assumption it is safe to measure the system's motion relative to the equilibrium position (rather than the un-stretched position of the springs). As demonstrated in my equilibrium video, when we measure from the equilibrium position the weight is offset by the force from the displacement of the springs.

This problem is the same as 3.23 in the 11th edition

For part B, the amplitude of the homogeneous response does not drop down to zero. The Yop you found is not the "steady state" amplitude as the amplitude of the response does not change with time.

You will need to use the homogeneous and particular response to find the amplitude.