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Question

# The angular frequency of small oscillations of the system shown in the figure is√(K/2m)√(2K/m)√(K/4m)√(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=X2Total energy of the system= Kinetic energy of block + spring energy,⇒12m˙X2+12KX21=ConstantPut the X1=X2⇒12m˙X2+18KX2=ConstantDifferentiating the equation,⇒m˙X¨X+14KX˙X=0 ⇒m¨X+14KX=0 ⇒¨X=−K4mX ⇒¨X=−ω2X,⇒Angular frequency ω=√K4m

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