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

# 3.13

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

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How can we solve for the peak amplitude without using a graphing software like MATLAB? If we were asked to solve for peak amplitude in an exam, do we just equate x_dot to zero and solve for t within each given interval and then substitute the value of that t in x(t) for the given time interval?

In most problems you will already have found the velocity; you could find the time when the velocity is zero then use that time to find the displacement. Alternately you can use your calculator to plot the displacement then use its built in functionality to find the maximum.

I'm a bit confused as to how you got that particular solution 5.152t/omega^2 *(t-2*zeta/omega)... In the text the table says at/w^2 which would give us the 5.152t/omega^2.

I just noticed that I was using the wrong table since there is damping.

what does it mean when the book asks to derive the EOM for: (i) the forced motion and (ii) the free motion?

This problem is the same as 3.13 in the 11th edition

how do we solve for the physical response of the system for a particular time interval

I don't understand your question. The solution at the bottom

isthe physical response foralltime.