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 in its plane keeping the strings tight . show that it will execute simple harmonic motion . find the time period .​

Answer 1

Solution :- Here we have to consider oscillation of centre of mass

Driving force F = mgsin¢

For small angle ¢ , sin¢ =¢

•°• a = g¢ = 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 Answer ✔

Answer 2

Answer:

2π√L/g

Explanation:

Driving force F = mg sin∅

Acceleration a = F/m = g sin∅

For small angle ∅, sin∅ = 0

∴ a = g ∅

    = g(x/L)

∴ a ∝ x

So, the motion is simple harmonic.

Time period T = 2π√Displacement/Acceleration

                       = 2π√L/g

Hope it helps!