Question

One end of a rod of length L is fixed to a point on the circumference of a wheel of radius R. The other end is sliding freely along a straight channel passing through the centre O of the wheel as shown in the figure. The wheel is rotating with a constant angular velocity $\omega$ about O. Taking $T=\frac{2\pi }{P\omega }$ the motion of the rod is?

• A. Simple harmonic with a period of T
• B. Simple harmonic with a period of $T/2$
• C. Not simple harmonic but periodic with a period of T
• D. Not simple harmonic but periodic with a period of $T/2$

Answer 1

The correct option is C Not simple harmonic but periodic with a period of T

In simple harmonic motion, oscillations occur about an equilibrium position where net force is zero. Also, at extreme positions, the object is stationary. Hence, the motion is not SHM.

The rod moves periodically because after each time period $T$, rod returns in the original position.