Question

A particle is executing simple harmonic motion. If the minimum time taken by the particle to move from extreme position to half of the amplitude is \( t_1 \), and the minimum time taken by the particle to move from mean position to half of the amplitude is \( t_2 \), then

• A. \( t_1 = t_2 \)
• B. \( t_1 = 0.5 t_2 \)
• C. \( t_1 = 2 t_2 \)
• D. \( t_1 = \sqrt{2} t_2 \)

Hint:

For simple harmonic motion, the time taken to cover specific parts of the oscillation depends on the position of the particle in the oscillation cycle.

Answer 1

The Correct Option is C

In simple harmonic motion, the time taken to move from extreme position to half the amplitude is \( t_1 \), which corresponds to a quarter of the period \( T \) of the oscillation. The time taken to move from mean position to half of the amplitude is \( t_2 \), which corresponds to half the period \( T \). Therefore, we can conclude: \[ t_1 = 2 t_2 \] Thus, the correct answer is: \[ \boxed{t_1 = 2 t_2} \]