JEE Advanced2016PhysicsOscillationsActual
A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x 0 . Consider two cases : (i) when the block is at x 0 ; and (ii) when the block is at x = x 0 + A . In both the cases, a particle with mass m < M is softly placed on the block after which they
Options
- AThe amplitude of oscillation in the first case changes by a factor of M m + M ′ whereas in the second ca
- BThe final time period of oscillation in both the cases is same
- CThe total energy decreases in both the cases
- DThe instantaneous speed at x 0 of the combined masses decreases in both the cases.
Correct answer
A. The amplitude of oscillation in the first case changes by a factor of M m + M ′ whereas in the second ca
Step-by-step solution
T i = 2 π M K , T f = 2 π M + m K Case (i): M A ω = M + m V ∴ Velocity decreases at equilibrium position. By energy conservation A f = A i M M + m Case (ii): No energy loss, amplitude remains same At equilibrium x 0 velocity = A ω In both cases ω decrease so velocity decreases in both cases