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[Solved] Mechanics of harmonic motion

I'm baffled by this mechanics question, since I don't entirely understand what it's asking, or how to answer it.

"A particle of mass m moves in one dimension under the action of a force given by -kx where x is the displacement of the body at time t, and k is a positive constant. Using F = ma write down a differential equation for x, and verify that its solution is x = Acos(wt + k), where w^2 = k/m. If the body starts from rest at the point x = A at time t = 0, find an expression for x at later times."

What does the question mean when it says to write down a differential equation for x? The best I could come up with was d^2x/dt^2 = -(k/m)x which gave me xlnx - lnx + cx + d = -(kt^2)/2m. Even if I made a mistake working that out it certainly isn't ever going to give me a cos function.
(edited 12 years ago)
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the bear
20
try using the solution x = Acos(wt + k)....differentiate it twice and see if it fits the equation d^2x/dt^2 = -(k/m)x which is quite correct.

:bear:
Reply 2
Avatar for 99wattr89
99wattr89
OP
4
Original post by the bear
try using the solution x = Acos(wt + k)....differentiate it twice and see if it fits the equation d^2x/dt^2 = -(k/m)x which is quite correct.

:bear:


Thanks very much!
I didn't think of working backwards form the answer. Instead I agonized over the question for half an hour!
Reply 3
Avatar for the bear
the bear
20
Original post by 99wattr89
Thanks very much!
I didn't think of working backwards form the answer. Instead I agonized over the question for half an hour!


if you see the word Verify it means check rather than prove the result

:bear:

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