COMEDK2015PhysicsOscillations
A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance X . Now, the combined mass will oscillate on the spring with period
Options
- AT=2 m g X(M+m)
- BT=2 (M+m) X m g
- CT= 2 m g X(M+m)
- DT=2 (M+m) m g
Correct answer
B. T=2 (M+m) X m g
Step-by-step solution
At initial condition of spring, M g=k X₀ ...(i) When mass m is added, then at equilibrium, (M+m) g=k (X+X₀ ) M g+m g=k X+k X₀ M g+m g=k X+M g [from Eq. (i)] m g=k X k= m g X ...(ii) Time period, aligned T &=2 Total mass of the block Force constant k &=2 M+m m g / X &=2 (M+m) X m g aligned