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COE in SHM

an elastic sp...

Question

an elastic spring of unstretched lenght L and force constant K is stretched by a small length C it is further stretched by a small length Y the qork done in seconh stretching is

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Solution

Work done in second stretching = Potential energy after second streching - Potential energy after first stretching

Potential energy stored, when it is extended by x, is
U₁= (1/2) k x²

Potential energy stored, when it is further extended by y, is
U₂ = (1/2) k (x+y)²

Work done = U2 - U1

= (1/2) k [x² +y² + 2xy - x²]

= (1/2) k*y ( 2x +y)

Answer : (1/2)ky(2x+y)

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