Question

.A particle is oscillating in simple harmonic motion. The time required for the particle to travel through one complete cycle is equal to the period of the motion, no matter what the amplitude is. But how can this be, since larger amplitudes mean that the particle travels farther?

The period is constant, but the angular frequency increases, so the particle travels farther.

The period is constant, but the average speed increases, so the particle travels farther.

The period is constant, but the mass increases, so the particle travels farther.

The period isn't constant. It increases also.

Answer 1

The period is constant, but the average speed increases, so the particle travels farther.

The time required for a particle in SHM to travel through one complete cycle is independent of the amplitude of the motion, even though at larger amplitudes the particle travels farther. This is possible, because at larger amplitudes, the maximum speed of the particle is greater. Thus even though the particle must cover larger distances at larger amplitudes, it does so with greater speeds.