How to calculate time for simple harmonic motion
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How to calculate time for simple harmonic motion

[From: ] [author: ] [Date: 12-11-01] [Hit: ]
The answer is 0.37 seconds.Please help!-What you did so far is fine.when x=A,when x=0,......
The question asks " how long does it take the blcok to move from x=A to x=0?"
I think we have to use this equation
x(t)=Acos ([sqr root k/m] time)

im having trouble rearranging the equation and Im not sure if this is right:
t= arccos (x/A) / sq root k/m

My amplitude is 0.7
K= 90 N/m
m= 5 kg
max speed = 3 m/s

The answer is 0.37 seconds.
Please help!

-
What you did so far is fine. Now just evaluate the arccos(x/A) at the two given positions;
when x=A, arccos(1) = 0
when x=0, arccos(0) = pi/2

So
tf - ti = (1/Sqrtk/m)(pi/2) - (1/Sqrtk/m)(0) = pi/2Sqrt(k/m)
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