Mechanical Resonance
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Mechanical Resonance. Natural frequency is the frequency that a system will oscillate / vibrate once it has been set into motion (given some energy and left alone). It depends on the its mass, shape, centre of mass and the material it is made from. (sometimes called resonant frequency).

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Mechanical Resonance

Natural frequency is the frequency that a system will oscillate / vibrate once it has been set into motion (given some energy and left alone). It depends on the its mass, shape, centre of mass and the material it is made from. (sometimes called resonant frequency)

next: damping


Un-damped SHM

damped SHM

highly damped SHM


Sometimes the oscillations happen due to the application of an external periodic force, then they are ‘driven oscillations’ or ‘forced oscillations’.

In this case the system oscillates at a different frequency, a combination of the natural frequency and the driving frequency.


Here the driving frequency is out of phase with the natural frequency.

natural frequency of the system

driving frequency of the applied force

resultant frequency of the driven system


Here the driving frequency is in phase with the natural frequency.

natural frequency of the system

driving frequency of the applied force

resultant frequency of the driven system

RESONANCE happens


The mass-spring system is attached to a vibration generator which is forcing it to oscillate (driving it).

We are varying the frequency of the vibration generator (driving frequency) and measuring the maximum amplitude of the oscillation each time.

This mass-spring system has a natural frequency of 3Hz.

Plotting a graph of the maximum amplitude of the driven system vs the driving frequency gives this graph:

If the system was heavily damped

maximum amplitude / m

0

1

2

3

4

5

6

driving frequency / Hz


maximum amplitude / m which is forcing it to oscillate (driving it).

0

1

2

3

4

5

6

driving frequency / Hz

When the driving frequency is below or above the natural frequency of the system, the amplitude is low.

When the driving frequency is equal to the natural frequency, the amplitude can be much higher

This ‘high amplitude response’ is called ‘resonance’

Resonance is the large amplitude oscillations that arise as a result of an oscillatory system being driven at a frequency equal to its natural frequency.

for highly damped systems, resonance becomes less noticeable.

Destructive resonance happens when the high amplitudes cause permanent damage to the system.


The gravitational field strength g on the Moon is one sixth that on Earth. A pendulum with a period of 1 s on Earth, would have, on the moon a period of :

a. 1/6 s

b. 1/√6 s

c. √6 s

d. 6 s




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