Question

A particle of mass 4 units moves along x axis attracted towards origin by a force with magnitude 8x.if it is initially at rest at x=10,then frequency of particle is

Answer 1

∴ The frequency of the particle is 1/(π√2) Hz.

Given:

The mass of the particle, m =  4 units.

The magnitude of the force of attraction, F = 8x.

The particle is initially at rest at x = 10.

To Find:

The frequency of the particle.

Solution:

We have been given that F = 8x.

⇒ F ∝ x

So this is the equation of simple harmonic motion.

In SHM, F = mω²x

m = mass of the particle.

ω = angular frequency of the particle

⇒ 8x = mω²x

⇒ 8 = mω²

⇒ ω = $\sqrt{\frac{8}{m} }$

We know that the angular frequency of the particle, ω = 2πf

⇒ f = 2π/ω

⇒ f =  $\sqrt{\frac{8}{m} }$ × 1/2π = 1/(π√2)

∴ The frequency of the particle is 1/(π√2) Hz.

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