1. Resonance Learning Objectives To Understand resonance
Book Reference : Pages 47-49
To Understand resonance
To be able to qualitatively explain how a system behaves at resonance and on either side of resonance in terms of amplitude & phase
To look at some real world examples of resonance

2. Resonance 1 Simple definition :
Resonance is the tendency of a system to oscillate with a larger amplitude at some frequencies than at others.
This particular frequency is called the resonant frequency & at this point the system is said to be in resonance
[Virtual Physics demo]

3. Resonance 2
This can be observed in many different types of oscillating systems :
What do the different colour lines represent?

4. Resonance 3 Consider a child being pushed on a swing in a playground.
The pushes are an example of an applied periodic force and the swing now experiences forced oscillations.
If timed correctly the pushes take the swing higher & higher

5. Resonance 4 (lightly Damped System)
Effect of Applied Frequency on amplitude :
Applied Frequency
Amplitude
Phase Difference*
Zero
< resonant frequency
Increasing more & more
Increases from zero towards /2 radians
At resonant frequency
(Applied frequency = Natural frequency)
Amplitude is at a significant maximum
/2 radians
> resonant frequency
Decreases more & more
Increases from /2 towards  radians
* Between the displacement and applied periodic force

6. Resonance 4 (lightly Damped System)
At resonance (assuming lightly damped):
Applied Frequency of Periodic Force  Natural Frequency of the system
The applied periodic Force is exactly in phase with the velocity of the system
The maximum amplitude is limited only by the damping in the system (why there are different colour plots on the earlier graphs)

7. Displacement & Velocity+
Amplitude
Displacement
Amplitude - T +
Velocity -

8. Displacement & Velocity 2
The change of velocity over time is given by the gradient of the displacement–time graph
The velocity is greatest when the gradient of the displacement-time graph is greatest (i.e. Zero displacement)
The velocity is zero when the gradient of the displacement-time graph is zero (i.e. Maximum displacement)
Think maths!! 1st differential of sin x is cos x

9. Damping
Increased damping causes the resonant frequency to fall below the natural frequency

10. Examples of Resonance Bridges Car suspension systems
[video : Tacoma Bridge.avi]
[video : London Millennium Bridge Opening.avi]
Car suspension systems
[animation: truck.swf]

11. Key Words 1 : Natural Frequency : Periodic Force
The frequency at which a system oscillates without an external periodic force being applied
Periodic Force
A force with a regularly changing amplitude & a definite time period

12. Key Words 2: Forced Oscillations: Resonance
The oscillations of a system which is exposed to an external periodic force
Resonance
For a lightly damped system, the amplitude of the oscillations tend to a maximum when the frequency of an applied periodic force is the same as the natural frequency of the system