Free and Forced Vibrations 16-17 Flashcards

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1
Q

What is a free vibration?

A

A spring vibrating in air.

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2
Q

What formula gives the total energy of a freely oscillating mass on a spring?

A

Etotal= 1/2mv2 + 1/2Kx2

(in other words, K.E + P.E)

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3
Q

A system can be forced to vibrate by a periodic external force.

The fequency of this force is called what?

A

Driving frequency.

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4
Q

When does a system resonate?

A

When the driving frequency approaches the natural frequency, the system gains more and more energy from the driving force and so vibrates with a rapidly increasing amplitude. When this happens the system is resonating.

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5
Q

Give examples of resonance.

A

1) The column of air resonates in an organ pipe, driven by the motion of air at the base.
2) A swing resonates if it’s driven by someone pushing it at its natural frequency.
3) A glass resonates when driven by a sound wave at the right frequency.
4) A radio is tuned so the electric circuit resonates at the same frequency as the radio station you want to listen to.

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6
Q

Why are some systems designed to experience damping forces?

A

Systems are often deliberately damped to stop them oscillating or to minimise the effect of resonance.

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7
Q

Given an example of a system in cars that uses damping.

A

Shock absorbers in a car suspension provide a damping force by squashing oil through a hole when compressed.

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8
Q

Draw a graph of light damping in an oscillating system.

A
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9
Q

Draw a graph of heavy damping in an oscillating system.

A
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10
Q

Draw a graph of critical damping.

A
  • Critical damping reduces the amplitude ( stopts the system oscillating) in the shortest possible time.
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11
Q

Draw a graph of an overdamped oscillating system.

A
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12
Q

Why are car suspension systems and moving coil meters critically damped?

A

They are critically damped so that they don’t oscillate but return to equilibrium as quickly as possible.

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13
Q

Why do lightly damped systems have a sharp resonance peak?

A

Their amplitude only increases dramatically when the driving frequency is very close to the natural frequency.

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14
Q

Why do heavily damped systems have a flatter response?

A

Their amplitude doesn’t increase very much near the natural frequency and they aren’t as sensitive to the driving frequency.

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15
Q

Draw the amplitude vs frequency of lightly damped oscillating systems and heavily damped oscillating systems.

A
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