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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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slide1

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

slide2

Un-damped SHM

damped SHM

highly damped SHM

slide3

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.

slide4

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

slide5

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

slide6

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

slide7

maximum amplitude / m

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.

slide8

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

slide9

A particle performs simple harmonic motion, has a period of 2 seconds and an amplitude of 4m.

  • The maximum acceleration of the particle is
  • a. Π ms-2
  • 4 Π ms-2
  • Π2 ms-2
  • Π2 ms-2
slide10

A lorry driver notices that the image in the rear-view mirror is blurred when the engine runs slowly and becomes clear as the engine speed is increased.

  • This is an example of
  • superposition
  • resonance
  • polarisation
  • coherence
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