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- √(K/2m)
- √(2K/m)
- √(K/4m)
- √(4K/m)

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Solution

Verified by Toppr

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

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