Assume a particle is moving with simple harmonic motion with its position governed by the equation

The velocity of the particle is defined to be the derivative . We define the frequency of the motion to be the reciprocal of the period.

Find the amplitude of the motion if the period is and the velocity is when .

Since the period is we have . Since when we have

Therefore,

Another way: y=Csin(kx + α) implies y=Bsin(kx)+Acos(kx), where A=f(0)=y0, B=f'(0)=+-v0. By definition C= sqr(A^2+B^2)=sqr(f0^2+v0^2).

My mistake: B*k=f'(0) so the period would have to be known1.