how do you show that the maximum speed of an oscillation in simple harmonic motion is the product of the angular velocity and the area?

Question

anonymous · Answer

It is not the angular velocity times the area. It is the angular velocity times the amplitude.
The equation for simple harmonic motion is 
$$x(t) = A \cos(\omega t)   _______   (1)$$
A is the amplitude, the maximum value of x
omega is the angular or circular frequency
From this you can get the velocity by differentiating with respect to t:
$$v(t) = dx/dt = - \omega A \sin(\omega t)    ________ (2)$$
From (2) you can see that the amplitude of the velovity, which is the maximim value of the speed is omega * A