8.5.3 Effect of Damping on Resonance

In a forced oscillation, the final amplitude reached is the amplitude at which the rate of gain of energy (from the driver) is matched by the rate of loss of energy (to the surrounding). It is kind of analogues to how the final terminal velocity is the velocity at which the weight is matched by the drag force.

Light damping is of course the reason for an oscillation to lose energy (to the surrounding). The resonance amplitude is thus dependent on the amount of light damping. (It is meaningless to talk about resonance for systems with heavy damping because there is no oscillation to talk about)

The resonance graphs under different amounts of light damping are shown below.

Notice that

• damping causes the entire resonance curve to be lower, not just at the resonance frequency, but at every frequency (except $\displaystyle f=0$).
• In theory, at zero damping, the resonance amplitude can reach infinity.
• Damping causes resonance to occur at a frequency slightly lower than the oscillator’s natural frequency. So the resonance peaks will shift towards lower frequency as damping increases. But the shift is not significant under very light damping conditions.
• Nearer to critical damping, the shift in the resonance frequency becomes obvious. But by then the resonance amplitude is so low it is not much of a resonance phenomenon.

Demonstration

SHM with Damping

Video Explanation

Effects of Damping on Resonance

Concept Test

1444