The kinetic energy of a particle executing S.H.M. is 16 J when it is at its mean position. If the amplitude of oscillations is 25 cm , and the mass of the particle is 5.12 kg , then the time period of the oscillation is

Question

The kinetic energy of a particle executing S.H.M. is 16 J when it is at its mean position. If the amplitude of oscillations is 25 cm , and the mass of the particle is 5.12 kg , then the time period of the oscillation is, 20 π s, 2 π s, π / 5 s, 5 π s

MARKS App · Accepted Answer

When the particle is in its mean position, the kinetic energy will be maximum, K max = 1 2 m ω 2 a 2 and ω = 2 π T ⇒ 16 = 1 2 × 5.12 × 4 π 2 T 2 × 0.25 2 ⇒ T 2 = 2.56 × 4 π 2 × 0.25 4 × 0.25 ⇒ T = 1.6 × 2 π × 0.25 4 = π 5 s

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