# PHY C13: Forced Oscillations

Now let’s look at the last type: Forced Oscillations

• Forced oscillations
• Natural Frequency
• Resonance
• Frequency Response
• Graphs

Let’s go!

What is a Forced Oscillation?
A type of oscillation where an external periodic force is being applied to a naturally vibrating system, causing it to vibrate with increasing amplitude.

What is Natural Frequency?
The frequency at which a freely oscillating system oscillates at without external force.

It is denoted by f0.

What is Resonance?
The phenomenon when a system oscillating at natural frequency is subjected to an external periodic force equal to the natural frequency, causing the system to vibrate with maximum amplitude.

What is Resonant Frequency?
The frequency of an external force which causes a system to exhibit resonance.
Usually this value is equal to the natural frequency, but it may vary due to damping.

What is Frequency Response?
Measure of amplitude of an oscillation against different applied frequencies.

• When the applied frequency is LESS than f0, the resulting amplitude is not maximum.
• When the applied frequency is EQUAL to f0, the resulting amplitude is maximum.
• When the applied frequency is MORE than f0, the resulting amplitude is not maximum.

This is represented by a RESONANCE CURVE:

What effect does Damping have on Frequency Response?
As damping increases:

• The amplitude of oscillations at all frequencies decreases
• The resonant frequency decreases (by a small amount)
• The peak becomes flatter

What are the effects of resonance?

 Positive Pushing a swing Tuning forks Musical instruments Negative Vehicle engines (causing mirrors to resonate) Bridge collapses (see Tacoma Narrows disaster)

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