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A body of mass 2 kg suspended through a vertical spring executes simple harmonic motion of period 4 s. If the oscillations are stopped and the body hangs in equilibrium, find the potential energy stored in the spring.

A body of mass 2 kg suspended through a vertical spring executes simple harmonic motion of period 4 s. If the oscillations are stopped and the body hangs in equilibrium, find the potential energy stored in the spring.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
7 years ago
Sol. m = 2kg. T = 4 sec. T = 2π √(m/k) ⇒ 4 = 2π √(2/k) ⇒ 2 = π √(2/k) ⇒ 4 = π2 (2/k) ⇒ k = 2 π2/4 ⇒ k = π2/2 = 5 N/m But, we know that F = mg = kx ⇒ x = mg/k = 2 x 10/5 = 4 ∴Potential Energy = (1/2) k x2 = (1/2) × 5 × 16 = 5 × 8 = 40J

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