Question

A flat horizontal platform moves up and down in S.H.M. with an amplitude of 1 cm. A small object is placed on the platform. What is the maximum frequency the platform can have, if the object is not to separate from it during any part of the motion ?

• A. $\frac{\sqrt{980}}{2\pi}$per second
• B. $\sqrt{980}/\sqrt{2\pi`}$ per second
• C. 980 / 2π per second
• D. 2 π× 980 per second

Answer 1

Answer: (A)

$\frac{\sqrt{980}}{2\pi}$per second

Answer 2

The maximum restoring force of S.H.M. is the weight of the object in the platform.

If A is the amplitude, we have mω²A = mg, where ω = 2π f. This solves to

f = $\frac{1}{2\pi}\sqrt{\frac{g}{a}} = \frac{1}{2\pi}\sqrt{980}$