Question

# Figure shows an ideal spring block system, force constant of spring is k which has been compressed by an amount x0. If x is instantaneous deflection of spring from its natural length, mark the correct option (s).

A
Instantaneous power developed by spring is P=kxkm(x20x2)
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B
Maximum power of spring is k2kmx20
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C
Maximum power occurs at x=x02
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D
Maximum power occurs at x=x02
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Solution

## The correct option is C Maximum power occurs at x=x0√2(A)−12k(x2−x20)=12mv2−0 ∴v=√km(x20−x2) ∴P=F.v=kx√km(x20−x2) (C)y=x20x2−x4 dydx=0⇒x=x0√2 ∴Pmax is at x=x0√2 (B)P=k√km(x20x2−x4) Pmax=k2√kmx20

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