A rectangular plate of sides a and b is suspended fropm a ceilling 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 harmonic motion. Find the time period.

Options

A. `2pisqrt((L)/(g))`
B. `2pi sqrt((L+a)/(g))`
C. `2pi sqrt((La)/(g.b))`
D. `2pi sqrt((La)/(g.d))`

Answer

A

Explanation

In displaced position `F_("restoring") = mg sin theta as theta` is small : `sin theta rarr theta, cos theta rarr 1`
`rArr F_(rest) = mg theta` and `theta = (x)/(L) rArr ma = mg((x)/(L))`
`rArr a = ((g)/(L)) x =omega^(2) x, omega = sqrt((g)/(L)), T = 2pi sqrt((L)/(g))`