Question

Does amplitude affect period$?$

Answer 1

No, the amplitude does not affect the period.

1. Amplitude is the distance from the center of motion to either extreme.
2. The period is the amount of time it takes for one complete cycle of motion.
3. Increasing the amplitude increases the distance to travel, but it also increases the restoring force, which raises the acceleration correspondingly.
4. This implies that the mass may cover a bigger distance at a faster rate.
5. Because these properties cancel each other out.

The equation of motion in SHM is given by

$y=A\sin (\omega t+\phi )$ ….(1)

Where,

$A=$ is the amplitude

$\omega =\frac{2\mathrm{\pi }}{T}$ ….(2)

Where, $T=$ time period

From equations (1) and (2), we can clearly see that

$T$ and $A$ are independent of each other.

Hence, the amplitude has no effect on the period.