Question

A rectangular plate of sides a and b is suspended from a ceiling by two parallel strings of length L each (figure 12-E11). 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, $F=mgsin\theta$

Acceleration = $a=\frac{8}{m}=gsin\theta$

$\therefore a=g\theta =g\left(\frac{x}{L}\right)$

[Where g and L are const.]

$\therefore a\alpha x$

So the motion is simple Harmonic.

Time period $t=2\pi \sqrt{\frac{\text{displacement}}{\text{Acceleration}}}$

$=2\pi \sqrt{\frac{x}{gx/L}}=2\pi \sqrt{\frac{L}{g}}$