# 19.2.2 Resonance

### Force Oscillations & Resonance

Some practical examples of forced oscillations and resonance include:

• The radio is “tuned” by setting its natural frequency equal to that of a radio station
• The resonance of the radio waves allows the signal to be amplified by the receiver to listen
• Microwave oven
• Conventional cooking methods involve transferring heat energy by conduction or convection
• A microwave transfers heat energy by radiation ie. microwaves of a particular frequency which resonate with the water molecules in food
• Magnetic resonance imaging (MRI)
• This type of scanner is a widely used medical diagnostic tool used to look at organs and structures inside the body
• The atomic nuclei in the body are made to resonate with incoming radio waves (of the order of 100 MHz)
• The signals are then sent to a computer to create digital scans and provide a detailed image of the scanned area

### Resonance

• In order to sustain oscillations in a simple harmonic system, a periodic force must be applied to replace the energy lost in damping
• This periodic force does work on the resistive force decreasing the oscillations
• These are known as forced oscillations, and are defined as:

Periodic forces which are applied in order to sustain oscillations

• For example, when a child is on a swing, they will be pushed at one end after each cycle in order to keep swinging and prevent air resistance from damping the oscillations
• These extra pushes are the forced oscillations, without them, the child will eventually come to a stop
• The frequency of forced oscillations is referred to as the driving frequency (f)
• All oscillating systems have a natural frequency (f0), this is defined as:

The frequency of an oscillation when the oscillating system is allowed to oscillate freely

• Oscillating systems can exhibit a property known as resonance
• When resonance is achieved, a maximum amplitude of oscillations can be observed
• Resonance is defined as:

When the driving frequency applied 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
• If the driving frequency does not quite match the natural frequency, the amplitude will increase but not to the same extent at 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
• 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
• 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 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

### Pros & Cons of Resonance

• Forced oscillations and resonance can be very useful when large-amplitude oscillations are intended
• However, large-amplitude oscillations can be very dangerous in structures, such as bridges, where resonance should be avoided

• Resonance is useful for:
• Producing ultrasound in a piezoelectric crystal
• Increasing the intensity of sound in musical instruments
• Pushing a child on a swing to make them go higher
• Resonance is a major component of machines and appliances such as:
• Microwave ovens
• Magnetic resonance imaging (MRI) scanners

• Resonance is a major concern in constructing structures, such as bridges and roofs
• An example of this is the Millennium Bridge in London which opened in June 2000:
• When pedestrians walked along the bridge, it began to sway from side to side
• The pedestrians therefore also swayed with the bridge in step, causing the amplitude of the bridge’s oscillation to gradually increase
• After closing for a few years, engineers eventually put ‘dampers’ on the bridge to absorb the energy of these oscillations
• Now the bridge is rigid and safe to walk on

### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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