Question

A particle moves in SHM such that its acceleration is a = -px, where x is the displacement of a particle from the equilibrium position and p is a constant. The period of oscillation is ______.

Options

• `(2pi)/sqrtp`

• `(2pi)/p`

• `2sqrt(pi/p)`

• `2pisqrtp`

Answer 1

A particle moves in SHM such that its acceleration is a = -px, where x is the displacement of a particle from the equilibrium position and p is a constant. The period of oscillation is `underlinebb((2pi)/sqrtp)`.

Explanation:

Given, acceleration, a = -px

Compared with the standard equation, we get

a = -ω²x

⇒ -px = -ω²x

⇒ ω² = p ⇒ ω = `sqrtp`

Now, a period of oscillation, T = `(2pi)/omega = (2pi)/sqrtp`