Question

How long a time in term of the period T does it take for a particle in harmonic motion to move from one extreme of its range to a point into the origin

Answer 1

Explanation:

The displacement equation x=A sinwt where A is the amplitude of oscillation

The particle is at mean position initially i.e at t=0, x=0

At the instant t, the particle is at a position of half amplitude i.e x=

2

A

∴

2

A

=A sinwt

0.5=sinwt ⟹wt=

6

π

T

2π

×t=

6

π

⟹t=

12

T