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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=x02
(A)12k(x2x20)=12mv20
v=km(x20x2)
P=F.v=kxkm(x20x2)

(C)y=x20x2x4
dydx=0x=x02
Pmax is at x=x02

(B)P=kkm(x20x2x4)
Pmax=k2kmx20

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