A rectangular plate of mass M, sides l1 and l2 is suspended from a ceiling by two parallel strings of length l3 each as shown in figure. The plate is displaced slightly in its plane keeping the strings tight. The angular frequency of its SHM is ω. Find the value of 2 ω2 in SI units. [. Take .: M=10 kg , l1=0.8 m , l2=0.2 m , l3=0.4 m ]

Question

A rectangular plate of mass M, sides l1 and l2 is suspended from a ceiling by two parallel strings of length l3 each as shown in figure. The plate is displaced slightly in its plane keeping the strings tight. The angular frequency of its SHM is ω. Find the value of 2 ω2 in SI units. [. Take .: M=10 kg , l1=0.8 m , l2=0.2 m , l3=0.4 m ] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The motion of the plate is translational motion.

For small angle

θ, 2 T = m g

2 T sin θ = ma

∴ m g (\frac{- x}{l}) = ma

\Rightarrow a = - \frac{g}{l} x = - ω^{2} x

\Rightarrow ω = \frac{g}{l}

The motion of the plate is translational motion. For small angle θ,2T=mg 2Tsinθ=ma ∴mg(l−x​)=ma ⇒a=−lg​x=−ω2x ⇒ω=lg​​

The motion of the plate is translational motion.

For small angle $θ, 2 T = m g$
$2 T sin θ = ma$
$∴ m g (\frac{- x}{l}) = ma$
$\Rightarrow a = - \frac{g}{l} x = - ω^{2} x$
$\Rightarrow ω = \frac{g}{l}$