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.
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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1 Answer
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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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