.) Potential energy of a particle performing linear S.H.M. is 0.1π2x2 joule. If mass of the particle is 20g, Find the frequency of S.H.M.
Answers
Given,
Potential energy of a particle performing linear Simple harmonic motion is 0.1π²x² Joule. mass of the particle is 20g.
To find,
The frequency of simple harmonic motion.
we know, potential energy of a particle performing S.H.M is given by, U = 1/2 mω²x²
where ω is angular frequency and x is displacement of particle.
on comparing,
we get, 0.1π² = 1/2 mω²
⇒0.1π² = 1/2 × (20 × 10¯³) × ω²
⇒0.1π² = 0.01ω²
⇒ω = √10π
⇒2πη = √10π
⇒η = √10/2 = √(5/2) sec
Therefore frequency of simple harmonic motion is √(5/2) sec.
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