In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillation will be :
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a
AM−mM
b
AMM+m
c
AMM−m
d
AM+mM
answer is B.
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Detailed Solution
Velocity at mean position is =AωConserving momentum MAω0=M+mV1⇒V1=MAω0M+m Also, New veloctiy at mean position =V1=A′ω1=A′KM+m⇒MAω0M+m=A′KM+m here, ω0=KM⇒A′=MAKMM+m×M+mK=AM(M+m)