(i) Define the damped harmonic motion and draw a simple figure showing how the amplitude m a damped harmonic motion decreases with time. (3 marks)

**Damped Harmonic Motion:**<br /><br />Damped harmonic motion refers to the oscillatory motion of a system in which the amplitude of oscillation decreases over time due to an external resistive force (such as friction or air resistance). This resistive force is proportional to the velocity of the object and acts in the opposite direction, causing the energy of the system to dissipate gradually.<br /><br />---<br /><br />**Figure:**<br />Below is a simple representation of how the amplitude of damped harmonic motion decreases with time:<br /><br />```<br />Amplitude<br /> |<br /> | * <br /> | * * <br /> | * * <br /> | * * <br /> | * *<br /> | * *<br /> | * *<br /> ----------------------------------> Time<br />```<br /><br />The curve shows that the amplitude diminishes exponentially over time.