The oscillation period is influenced by damping, leading to a reduction in its duration.

When a system experiences damping, the amplitude of its oscillations diminishes over time. This phenomenon occurs due to the dissipation of energy as the system transfers energy to its surroundings. Consequently, the period of oscillation is impacted, resulting in a decrease.

To illustrate this, let’s examine a simple harmonic oscillator with damping. The equation of motion for such a system can be expressed as:

In this equation, $m$ represents the mass of the oscillator, $c$ is the damping coefficient, $k$ denotes the spring constant, and $x$ is the displacement from the equilibrium position.

The solution to this differential equation is given by:

Here, $A$ and $B$ are constants determined by the initial conditions, and $w_d$ is the damped natural frequency, defined as:

From this expression, we can observe that the damped natural frequency $w_d$ is less than the undamped natural frequency $\sqrt{\frac{k}{m}}$ due to the presence of the damping term. This implies that the period of oscillation, which is inversely related to the frequency, also decreases as a result of damping.

In summary, damping not only causes the amplitude of oscillations to reduce over time but also affects the period of oscillation, leading to a decrease in its duration.