Question

Which of the following figures represents damped harmonic motion?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

The oscillations in which the amplitude decreases gradually with the passage of time are called damped oscillations.

Equation of a damped oscillation is given by $y=A_0{e}^{-\gamma t}\sin ({\omega }^{\prime }t+\varphi )$
This equation will be satisfied by the graph in option (a).

Graph in option (b) represents motion of a particle with variations in amplitude, but the amplitude of oscillations doesn't continuously decrease with time. So, option (b) is a wrong answer.

Graph in option (c) represents a particle whose amplitude increases with time and becomes constant at steady state. So, option (c) is also wrong.

Graph in option (d) represents a particle whose amplitude decreases with time exponentially but has no oscillatory motion. Hence, option (d) is also wrong.
Thus, option (a) is the correct answer.