# 5.6.5 Examples of Forced Oscillations & Resonance

## Examples of Forced Oscillations & Resonance

• Resonance occurs for any forced oscillation where the frequency of the driving force is equal to the natural frequency of the oscillator
• For example, a glass smashing from a high pitched sound wave at the right frequency
• Some other practical examples of forced oscillations and resonance include:
• An organ pipe
• Microwave oven
• Magnetic resonance imaging (MRI)
• In an organ pipe
• Air molecules vibrate in an air column setting up a stationary wave in the pipe
• This causes the air molecules to resonate leading to an increase in amplitude of sound

Standing waves forming inside an organ pipe from resonance

• The radio is “tuned” by setting its natural frequency equal to that of a radio station
• The radio tuned so that the electric circuit resonates at the same frequency as the specific broadcast
• 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 i.e. microwaves of a particular frequency that 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

#### Barton's Pendulums

• A mechanical system commonly used to show resonance is Barton's pendulums
• A set of light pendulums labelled A-E are suspended from a string
• A heavy pendulum X, with a length L, is attached to the string at one end and will act as the driving pendulum

• When pendulum X is released, it pushes the string and begins to drive the other pendulums
• Most of the pendulums swing with a low amplitude but pendulum C with the same length has the largest amplitude
• This is because its natural frequency is equal to the frequency of pendulum X (the driving frequency)

Barton's pendulums helps display resonance

• The phase of the oscillations relative to the driver are:
• Pendulums E and D with lengths < L are in phase
• Pendulum C with length = L is 0.5π out of phase
• Pendulums B and A with lengths > L are π out of phase

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