Question

The time period of a particle in simple harmonic motion is equal to the smallest time between the particle acquiring a particular velocity v. The value of v is
(a) v max.
(b) 0
(c) between 0 and v max.
(d) between 0 and -v max.

Answer 1

Answer ⇒ Option (a). V max.

Explanation ⇒ Time Period means the total time required by the particle in Simple Harmonic Motion, to returns to the same place from where where it is started and it should be in the same direction.

We know velocity is a vector quantity, it depends upon both, the magnitude as well as the direction.

Now, when the Particle starts from the mean position it was having the maximum velocity which is directed towards one of the extreme. Now, it reaches that extreme and its velocity becomes zero. Then it started moving from there, and returns to the mean position again but is direction is opposite so velocity will not be same at that point, and then it moves to another extreme from where it comes to means again, and now, its direction will be same as that of the initial, that is maximum velocity.

This means, Velocity at that position is v max. The Particle repeats its after one time period.

Hence, it s the correct answer.

Hope it helps.