A body is executing a linear S.H.M. Its potential energies at the displacement ' x ' and ' y ' are ' E₁ ' and ' E₂ ' respectively. Its potential energy at displacement (x+y) will be (a) E₁ + E₂ (b) (√(E₁) + √(E₂))² (c) E₁ - E₂ (d) (√(E₂) - √(E₁))²

Answer: (b). x = √(2E₁/k), y = √(2E₂/k) E = 1/2k(x + y)² = (√(E₁) + √(E₂))² So the answer is (b).

A body is executing a linear S.H.M. Its potential energies at the… | MHT CET 2023 (10 May, Shift 2)

Q44MHT CET 2023 · 10 MAY · SHIFT 2Medium

Energy in SHM

A body is executing a linear S.H.M. Its potential energies at the displacement ' $x$ ' and ' $y$ ' are ' $E_1$ ' and ' $E_2$ ' respectively. Its potential energy at displacement $(x+y)$ will be

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Answer: (b)

$x = \sqrt{\frac{2E_1}{k}}$ , $y = \sqrt{\frac{2E_2}{k}}$
$E = \frac{1}{2}k(x + y)^2 = \left(\sqrt{E_1} + \sqrt{E_2}\right)^2$
So the answer is (b).

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Energy in SHM question from MHT CET 2023 (10 May, Shift 2)

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