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Question

The angular frequency of small oscillations of the system shown in the figure is
598949_f813036272664ce18f4f82a0fc10f6d5.png
  1. (K/2m)
  2. (2K/m)
  3. (K/4m)
  4. (4K/m)

A
(K/4m)
B
(K/2m)
C
(2K/m)
D
(4K/m)
Solution
Verified by Toppr

The correct option is C (K/4m)
Let block of mass m is pulled down by X due to this spring is stretched by X1.
From string constraint 2X1=X X1=X2
Total energy of the system= Kinetic energy of block + spring energy,
12m˙X2+12KX21=Constant
Put the X1=X2
12m˙X2+18KX2=Constant
Differentiating the equation,
m˙X¨X+14KX˙X=0 m¨X+14KX=0 ¨X=K4mX ¨X=ω2X,
Angular frequency ω=K4m

935383_598949_ans_d2bf58d27ef4407b8706e764aa8cbbf0.JPG

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