Consider the figure here. A particle of mass m is constrained to move inside a smooth vertical groove of radius R and is connected to a light spring of spring constant K in equilibrium. O is centre of

Question

Consider the figure here. A particle of mass $m$ is constrained to move inside a smooth vertical groove of radius $R$ and is connected to a light spring of spring constant $K$ in equilibrium. $O$ is centre of the groove. $x$ and $y$ are horizontal and vertical axes respectively. Different physical parameters are related as $2 KR = 7 mg$ . Angular frequency of the oscillations, if the particle is slightly displaced from the shown equilibrium position is

TestHub · Accepted Answer

Restoring torque on small displacement d θ τ = K R 2 d θ + m g 2 R d θ ⇒ α = τ l = K R 2 + m g 2 R d θ m R 2 = K m + g 2 R d θ = ω 2 d θ ⇒ ω = K m + g 2 R = 2 g R

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