How is the period of oscillation affected by damping?

The period of oscillation is affected by damping, causing it to decrease.

When a system undergoes damping, the amplitude of the oscillation decreases over time. This is due to the dissipation of energy as the system loses energy to its surroundings. As a result, the period of oscillation is affected, causing it to decrease.

To understand this, consider a simple harmonic oscillator with damping. The equation of motion for this system is given by:

m(d^2x/dt^2) + c(dx/dt) + kx = 0

where m is the mass of the oscillator, c is the damping coefficient, k is the spring constant, and x is the displacement from equilibrium.

The solution to this equation is given by:

x(t) = e^(-ct/2m) [A cos(wd t) + B sin(wd t)]

where A and B are constants determined by the initial conditions, and wd is the damped natural frequency given by:

wd = sqrt(k/m - (c/2m)^2)

From this equation, we can see that the damped natural frequency is less than the undamped natural frequency (sqrt(k/m)) due to the presence of the damping term. This means that the period of oscillation is also affected, causing it to decrease.

In summary, damping causes the amplitude of oscillation to decrease over time, which in turn affects the period of oscillation, causing it to decrease.