5. Forced Oscillations and Resonance

What are Forced Oscillations?

Produced when a body is subjected to a periodic external driving force and made to oscillate at the frequency of the driving force (which may not be its natural frequency).

What is a Driver?

The system providing the periodic external driving force.

What is Resonance?

Occurs when the frequency of the driving force is close to or at the natural frequency of the driven system. There is maximum transfer of energy from the driver, and the system responds with maximum amplitude.

What affects the amplitude of a forced oscillation? (Factors affecting Amplitude)

The damping of the system, and the relative values of the driving frequency (f) and the natural frequency (f₀).

When do oscillations with maximum amplitude (resonance) occur?

When the driving frequency (f) is close to or at the natural frequency (f₀) of the system.

What determines the sharpness of frequency response curves at resonance? (Degree of Damping)

The degree of damping.

What is the effect of No Damping on Resonance?

Resonance occurs at f = f₀. Amplitude is infinite.

What is the effect of Light Damping on Resonance?

Resonance occurs at f ≈ f₀. Amplitude is large but decays rapidly when f deviates from f₀. Resonance peak is sharp.

What is the effect of Increasing Damping (still light) on Resonance?

Resonance occurs at lower frequency and with smaller maximum amplitude. Resonance peak broadens.

What is the effect of Critical Damping on Resonance?

Frequency response curve is relatively flat.

When is Resonance Useful?

In various applications (mechanical, electromagnetic, acoustic, nuclear magnetic resonance) where energy transfer and amplification are desired.

What are some applications where Resonance is Useful?

Radio receiving aerials (tuning circuitry amplifies signal), microwave cooking (water molecules absorb energy), string instruments (acoustic resonator amplifies sound), MRI (nuclear magnetic resonance).

When is Resonance Not Useful/should be avoided?

In mechanical structures (bridges, buildings, aeroplanes) where strong external driving forces matching natural frequencies can cause rupture.

What are some examples where Resonance is NOT useful?

Angers bridge collapse (soldiers marching), Tacoma Narrows Bridge collapse (wind-induced oscillations), Mexico earthquake (buildings collapse due to seismic waves matching natural frequency), bus body vibrations at engine speed.

How do engineers prevent destructive resonance?

By conducting elaborate vibration tests on models of structures (bridges, buildings, aeroplanes) to ensure designs prevent large amplitudes.