# Simple pendulum with initial velocity

I’ve attached a couple questions just because these are the type of questions I’ve had some difficulty solving since I don’t recall addressing anything too similar too similar in the past (i.e., changing velocity and determining how the amplitude varies because of this). I know to go from x(t) to v(t) you take the derivative, and that x(t) = x_{m}cos(ωt + ø) in general. Then v(t) = -ωx_{m}sin(ωt + ø). When looking at questions similar to 39, when I see v_{o} is now 4v_{o} and asking for the amplitude change to be determined, I look at x_{m}. This means the new amplitude would have to be 4x_{m} since all other variables are being kept constant, no? Also, once again taking the derivative to find a(t), wouldn’t the acceleration be 4 times as great once again?

Is there any other fundamental expression relating amplitude with velocity or frequency or any other variable as in question 21 or in general? Once again, I am also slightly confused on how exactly question 25 was solved too. If there any good online sources I could be referred to that would be greatly appreciated! If I am just missing something here and if someone could point out what I am not looking at, that would be amazing too!

Thanks!

http://ift.tt/1kJz0SE

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