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

The correct answer is

(a) v_max  

Explanation:

Velocity is a vector, means it has magnitude as well as direction. The maximum velocity at the mean position is acquired by the particle after a single time period at the same position. Other velocities occur twice between one extreme to other extreme position (i.e. within half a time period, See picture below). Hence only (a) true, others not true.