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 simply harmonic motion. Find the time period.

• A. $2\pi \sqrt{\frac{b}{g}}$
• B. $2\pi \sqrt{\frac{a}{g}}$
• C. $2\pi \sqrt{\frac{L}{g}}$
• D. $2\pi \sqrt{\frac{d}{g}}$

Answer 1

The correct option is C

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

mg sin$\theta$ provides the necessary torque

=-mg sin $\theta$=ma

$-mg\frac{x}{L}=ma$

$-\frac{g}{L}x=a$

$\omega =\sqrt{\frac{g}{L}}$

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