Harmonic oscillator

Classical Mechanics Level 2

When we light a parallel ray on the object( $P$ ) which is in uniform circular motion with angular velocity $\omega$ , the motion of its shadow( $Q$ ) on the right side screen is a harmonic oscillation. What are the displacement(vector) and period, respectively, of the harmonic oscillation of the shadow( $Q$ ) at time $t$ as shown above?

A\cos \omega t

\frac{2\pi}{\omega}

A\cos \omega t

2\pi\omega

A\sin \omega t

2\pi\omega

A\sin \omega t

\frac{2\pi}{\omega}

1 solution

Yash Srivastava
Mar 13, 2014

Since displacement is repeating its values periodically hence it should be a sine or cosine function. If the shadow is at position Q, then the component of its vector from the center (O) of the circle along the perpendicular to the parallel rays is A sin(ωt), where 'A' is the radius of the circle and 'ωt' is the angle of the vector OQ with the vector along parallel rays. Time period is given by 2π/ω as angular velocity(ω) = 2π radiant /time (speed =distance /time) hence time(t) =2π/ω.

Harmonic oscillator

1 solution

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