Question

A rectangular plate of sides $a$ and $b$ is suspended from a ceiling by two parallel strings of length $L$ each. The separation between the strings is $d$. The plate is displaced slightly in its plane keeping the strings tight. Show that it will execute simple harmonic motion. Find the time period.

Answer 1

Here we have to consider oscillation of centre of mass

Hence,

Driving force $F=mgsin\theta$

For small angle $\theta ,sin\theta \approx \theta$

So, $a=g\theta =g\frac{x}{L}$ [where g and L is constant ]

$\Rightarrow$ $aisproportionaltox$

So the motion is simple harmonic

Time period , $T=2\pi \sqrt{\frac{dispalcement}{acceleration}}$

$T=2\pi \sqrt{\frac{L}{g}}$