Question

A rectangular plate of sides $a$ and $b$ is suspended from a ceiling by two parallel strings of length $L$ each (figure). 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

Driving force F = mgsin(θ)

For small angle θ , sinθ =θ

So, a = gθ= g(x/L) [where g and L is constant ]

a proportional x

so the motion is simple harmonic

Time period , T = 2π√dispalcement / acceleration

T = 2π √x/(gx/L)

T = 2π√L/g