# Maximum speed of sinusoidal vibration in s.h.m.

#### Bugsy23

1. The problem statement, all variables and given/known data
I need to find the maximum speed of a hydraulic valve component which is attached to a vibration testing machine and subjected to sinusoidal vibrations. The values I have so far are the frequency of vibration, the period of motion, the acceleration amplitude and the vibration amplitude.
2. Relevant equations
The only equation I have found for calculating speed in simple harmonic motion is
v=d(x)/d(t)
3. The attempt at a solution
I assume the change in time would be the same as the period of motion. Would the change in position (x) then be equal to the vibration amplitude?

(If anyone knows how to calculate the maximum acceleration, given the maximum speed, that would also be very helpful. Thanks)

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#### housemartin

well if you have sinusoidal vibrations, period of motion and acceleration amplitude, you can write acceleration as:
a = a0*sin(2*pi*t/T)
a0 - amplitude of acceleration t - time, T - period.
from here by integration you can find velocity and its maximum value.
but i did not quite understood your problem ;]

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"Maximum speed of sinusoidal vibration in s.h.m."

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