Simple Harmonic Motion - Average Speed · PhysicsBowl 2015 #26

Physics · mechanics

Problem

The position of a mass connected to a spring obeys

x(t) = A\cos(\omega t)

. What is the average speed of the mass for one full oscillation in terms of the mass's maximum speed during oscillation,

v_{max}

? (A)

\frac{2}{\pi}v_{max}

(B)

\frac{1}{\sqrt{2}}v_{max}

(C)

\frac{1}{2}v_{max}

(D)

\frac{\sqrt{2}}{\pi}v_{max}

(E)

\frac{1}{2\pi\sqrt{2}}v_{max}