Question

A large horizontal surface moves up and down in $S.H.M.$ with an amplitude of $1cm$. If a mass of $10kg$ (which is placed on the surface $0$ is to remain continuously in contact with it, the maximum frequency of $S.H.M.$ will be

• A. $5Hz$
• B. $0.5Hz$
• C. $1.5Hz$
• D. $10Hz$

Answer 1

The correct option is A $5Hz$

Frequency of SHM,
$v=\frac{1}{2\pi }\sqrt{\frac{acceleration}{displacement}}=\frac{1}{2\pi }\sqrt{\frac{a}{x}}$
$\Rightarrow v=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$
$\Rightarrow \frac{k}{m}=\frac{a}{x}\Rightarrow \frac{k}{a}=\frac{m}{x}\Rightarrow v=\frac{1}{2\pi }\sqrt{\frac{m}{x}}$
$v=\frac{1}{2\pi }\sqrt{\frac{10}{{10}^{-2}}}=\sqrt{\frac{{10}^3}{2\pi }}=\frac{10\sqrt{10}}{2\pi }$$=\frac{10\times 3.16}{2\times 3.14}=5Hz$