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

# 3.12

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

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for the final answer I believe it should be e^(-2.598(t-.917)) for t>.917 correct?

That is correct should appear on the last line.

why is it that you defined g(t) in mm/s^2? shouldnt it be m/s^2? 350 kg-m/s^2 / 50 kg

You are correct, the definition of g(t) should have the units of m/s^2. The unit of A stands as millimeters though.

When it says, "solve for motion for the time interval 0 < t < 1.5s," should I plug 1.5 in for t for the very bottom row of x(t)? I'm just trying to clarify that I understand the phrasing, "solve for motion."

"Solve for the motion" implies that you should find the function (in this case ) that describes the motion. Stating a position function which is valid for the entire timespan is sufficient.

This problem is the same as 3.12 in the 11th edition

In the textbook it asks for peak response- is this when velocity=0? How do we solve for this?

The "peak response" refers to the farthest distance that the body travels (from equilibrium) at any point in its motion. So, generally thinking about these kinds of problems requires thinking about what the motion looks like (by graphing position as a function of time) and deciding which point is farthest from the equilibrium line. If you were to solve for this quantity using a system of equations involving the velocity and position functions then you would solve the velocity equation for time when the velocity itself is zero, then plug that value (in this case values) into the position equation. It is still left to you to decide witch time is the correct one to plug in to the position equation; this will always require a plot of the position vs time.

edit: for a plot of the position as a function of time click on the little radio button above that says "childs-3-12_plot.png", it is much easier to see where the peak response is when graphed.