Question

What is the ratio between the distance travelled by the oscillator in one time period and amplitude?

Answer 1

In the diagram shown a particle is executing SHM between P and Q. The particle starts from the mean position ‘O’ and moves to amplitude position ‘P’, then the particle turns back and moves from ‘P’ to iQ Finally the particle turns back again and returns to mean position ‘O’. In this way, the particle completes one oscillation in one time period.

Total distance travelled while it goes from O → P → O → Q → O

= OP + PO + OQ + QO

= A + A + A + A

= 4A

Amplitude = OP = A

Hence, the ratio of distance and amplitude = 4A/A = 4.