Question

potential energy of a particle performing linear S.H.M is 0.1π^2x^2 joule .if mass of the particle is 20g find the frequency of S.H.M​

Answer 1

Given : potential energy of a particle performing linear S.H.M is 0.1π²x² joule. and the mass of the particle is 20g.

To find : The frequency of simple harmonic motion.

solution : Potential of a particle performing linear SHM is U = 0.1π²x²

but we know, potential energy is given by, U = 1/2 mω²x²

putting, m = 20g = 0.02 kg

now, U = 1/2 × 0.02 ω²x² = 0.1 π²x²

⇒0.01ω² = 0.1π²

⇒ω² = 10π²

⇒ω = √(10) π

⇒2πη= √(10) π

⇒η= √10/2 = √(5/2) Hz

Therefore frequency of the simple harmonic motion is √(5/2) Hz.

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