Question

# Which of the following figures represents damped harmonic motion?

A
B
C
D

Solution

## 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=A0e−γtsin(ω′t+ϕ) 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.

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