A vibrating wire is executing simple harmonic motion (that is, is aharmonic osci

Question

A vibrating wire is executing simple harmonic motion (that is, is aharmonic oscillator). If the amplitude of the oscillation is0.5mm, and the speed of the wire as it passes through the center ofits motion is 15 m/s, what frequency, f = /(2), is itvibrating at?

So far this is what I have come up with:

x(t) = Asin(t + ) = acos(t) + bsin(t)
v(t) = dx/dt = -asin(t) + bcos(t) =(bcos(t) - asin(t))

v(t) = 15 m/s when x(t) = 0

A = (a2+ b2)
tan = a/b
a = Asin
b = Acos

Also
x(0) = a
v(0) = b

Unsure of how to apply what I have ... help!! will ratelifesaver

Explanation / Answer

Don't overthink this... for an object in SHM, the max speedoccurs when it passes through the center, and the max speed isgiven by .     v max = A      where    = 2f . So...    v max = A 2 f .     f = v max / 2 A =   15 m/s / 2 * 0.0005 m =   4775 Hz

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