Question

While a particle executes linear simple harmonic motion:

• A. Its linear velocity and acceleration passes through their maximum and minimum values once, in each
  oscillation
• B. Its linear velocity and acceleration passes through their maximum and minimum values twice, in each
  oscillation
• C. Its linear velocity and acceleration passes through their maximum and minimum values four times, in each
  oscillation
• D. Its linear velocity and acceleration always attains their peak values simultaneously.

Answer 1

Answer: (B)

Its linear velocity and acceleration passes through their maximum and minimum values twice, in each

oscillation
The velocity is minimum (zero) at the extreme position and maximum $(\pm \omega A)$ at the mean position.
The acceleration is minimum $(\pm {\omega }^{2}A)$ at the extreme position and minimum (zero) at the mean position. Since the particle crosses the mean and extreme positions twice, during each oscillation, hence the result.