A horizontal board is performing simple harmonic oscillations horizontally with an amplitude 0.3 m and a…
A horizontal board is performing simple harmonic oscillations horizontally with an amplitude 0.3 m and a period of 4 s . The minimum coefficient of friction between a heavy body placed on the board if the body is not to slip is.
$\mu=0.05$
$\mu=0.075$
$\mu=0.173$
$\mu=1.14$
Solution
The maximum acceleration of oscillation,
$\begin{aligned}
& a_{\max }=\omega^2 A \Rightarrow \mu g=\left(\frac{2 \pi}{T}\right)^2 A \\
& \Rightarrow \mu=\frac{4 \pi^2 \times 0.3}{(4)^2 \times 10}=0.075
\end{aligned}$