A simple pendulum of length and bob mass undergoes small angular displacements in a…

PHYSICS · Single correct · CBSE · Physics · Oscillations · Oscillations

Problem

A simple pendulum of length

l

and bob mass

m

undergoes small angular displacements

\theta(t)

in a vertical plane. A damping torque proportional to angular velocity with coefficient

\beta

acts on the bob, and an external horizontal force

F_0\sin \omega_d t

is applied at the bob. Under the small-angle approximation (

\sin\theta\approx\theta

), which of the following equations best represents its angular motion? (a)

m l^{2}\,\ddot\theta + \beta\,\dot\theta + m g l\,\theta = F_0 l\sin \omega_d t

(b)

m l^{2}\,\ddot\theta + \beta l^{2}\,\dot\theta + m g l\,\theta = F_0 l\cos \omega_d t

(c)

m l^{2}\,\ddot\theta + \beta l^{2}\,\dot\theta + m g l\,\theta = F_0 l\sin \omega_d t

(d)

m l^{2}\,\ddot\theta + \beta l^{2}\,\dot\theta + m g l\,\theta = F_0 l\sin 2\omega_d t