An object of mass 0.5 kg executing simple harmonic motion. Its amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant t = T/4 s starting from mean position. Assume that the initial phase of the oscillation is zero.

Option 1 - 6.2 × 10⁻³ J

Option 2 - 0.62 J

Option 3 - 6.2 × 10³ J

Option 4 - 1.2 × 10³ J

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Vishal Baghel | Contributor-Level 10

5 months ago

Correct Option - 3

Detailed Solution:

T = 2π√ (m/k)
0.2 = 2π√ (0.5/k)
k = (0.5) (2π/0.2)² = 50π² ≈ 500
x = A sin (ωt) = 5 sin (2π/T * t)
At t=T/4, x = 5 sin (π/2) = 5cm
PE = ½kx² = ½ * 500 * (0.05)² = 250 * 0.0025 = 0.625 J

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