# Resonance(OCR A Level Physics)

Author

Katie M

Expertise

Physics

## Resonance

• The frequency of forced oscillations is referred to as the driving frequency, f, or the frequency of the applied force
• All oscillating systems have a natural frequency, f0, this is defined as this is the frequency of an oscillation when the oscillating system is allowed to oscillate freely
• Oscillating systems can exhibit a property known as resonance
• When the driving frequency approaches the natural frequency of an oscillator, the system gains more energy from the driving force
• Eventually, when they are equal, the oscillator vibrates with its maximum amplitude, this is resonance

• Resonance is defined as:

When the frequency of the applied force to an oscillating system is equal to its natural frequency, the amplitude of the resulting oscillations increases significantly

• For example, when a child is pushed on a swing:
• The swing plus the child has a fixed natural frequency
• A small push after each cycle increases the amplitude of the oscillations to swing the child higher. This frequency at which this push happens is the driving frequency
• When the driving frequency is exactly equal to the natural frequency of the swing oscillations, resonance occurs
• If the driving frequency does not quite match the natural frequency, the amplitude will increase but not to the same extent as when resonance is achieved

• This is because, at resonance, energy is transferred from the driver to the oscillating system most efficiently
• Therefore, at resonance, the system will be transferring the maximum kinetic energy possible

## Amplitude-Frequency Graphs

• A graph of driving frequency f against amplitude A of oscillations is called a resonance curve. It has the following key features:
• When f < f0, the amplitude of oscillations increases
• At the peak where f = f0, the amplitude is at its maximum. This is resonance
• When f > f0, the amplitude of oscillations starts to decrease

The maximum amplitude of the oscillations occurs when the driving frequency is equal to the natural frequency of the oscillator

#### The Effects of Damping on Resonance

• Damping reduces the amplitude of resonance vibrations
• The height and shape of the resonance curve will therefore change slightly depending on the degree of damping
• Note: the natural frequency f0 of the oscillator will remain the same

• As the degree of damping is increased, the resonance graph is altered in the following ways:
• The amplitude of resonance vibrations decrease, meaning the peak of the curve lowers
• The resonance peak moves slightly to the left of the natural frequency when heavily damped

• Therefore, damping reduced the sharpness of resonance and reduces the amplitude at resonant frequency

As damping is increased, resonance peak lowers, the curve broadens and moves slightly to the left

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