The balance wheel of a watch vibrates with an angular amplitude theta0, angular

Question

The balance wheel of a watch vibrates with an angular amplitude theta0, angular frequency w, and phase angle theta = 0. Find an expression lor the angular velocity dtheta/dt as a function of time. Express your answer in terms of the given quantities. Find an expression for the angular acceleration d^2theta/dt^2 as a function of time. Express your answer in terms of the given quantities. Find the balance wheel's angular velocity when its angular displacement is theta0. Express your answer in terms of the given quantities.

Explanation / Answer

theta = theta_o*cos(wt+phi)

A) (d/dt)(theta) = -theta_0*w*sin(wt)

B) (d^2/dt^2)(theta) = -theta_0*w^2*cos(wt)

C) at the angular displacement theta_0

angular velocity is (d/dt)(theta) = 0 rad/s

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