Equilibrium Constant and Standard Free Energy Change
Find the natu...
Question
Find the natural frequency of the system shown in the figure. The pulleys are smooth, massless and the spring is unstretched in the equilibrium position.
A
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B
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C
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D
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Solution
The correct option is A Let x be the displacement of the block from the equilibrium position. Since the length of the string remains the same, the spring extends by x = (2x). The energy of the system is E=12kx2+12mv2=12k(2x)2+12mv2 Differentiate with respect to time dEdt−4kxdxdt+mvdvdt=0 (energy conservation) ⇒4kxv+mvd2xdt2=0 ∴4kg+md2xdt2=0⇒d2xdt2+4kxm=0 ∴T=2π√m4k=π√mk