SHMHard

Question

A bob of mass 2m hangs by a string attached to the block of mass m of a spring block system. The whole arrangement is in a state of equilibrium. The bob of mass 2m is pulled down slowly by a distance x0 and released.

Options

A.For x0 = maximum tension in string is 4mg
B.For x0 = , minimum tension in string is mg
C.Frequency of oscillation of system is , for all non-zero values of x0
D.The motion will remain simple harmonic for x0 ≤

Solution

           
(A) kx = 3 mg; equilibrium
k (x + x0) - T - mg = ma        ......(1)
T - 2 mg = 2 ma          .....(2)
On solving,
T =
for x0 =

T = 4 mg
(D) If x0 =
If x0 = then string will become slack when ′m′ comes to rest at top most extreme possible.]

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