# 19.2.1 Damping

### Damping

• In practice, all oscillators eventually stop oscillating
• Their amplitudes decrease rapidly, or gradually
• This happens due to resistive forces, such friction or air resistance, which act in the opposite direction to the motion of an oscillator
• Resistive forces acting on an oscillating simple harmonic system cause damping
• These are known as damped oscillations
• Damping is defined as:

The reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system

• Damping continues until the oscillator comes to rest at the equilibrium position
• A key feature of simple harmonic motion is that the frequency of damped oscillations does not change as the amplitude decreases
• For example, a child on a swing can oscillate back and forth once every second, but this time remains the same regardless of the amplitude

#### Exam Tip

Make sure not to confuse resistive force and restoring force:

• Resistive force is what opposes the motion of the oscillator and causes damping
• Restoring force is what brings the oscillator back to the equilibrium position

### Types of Damping

• There are three degrees of damping depending on how quickly the amplitude of the oscillations decrease:
• Light damping
• Critical damping
• Heavy damping

#### Light Damping

• When oscillations are lightly damped, the amplitude does not decrease linearly
• It decays exponentially with time
• When a lightly damped oscillator is displaced from the equilibrium, it will oscillate with gradually decreasing amplitude
• For example, a swinging pendulum decreasing in amplitude until it comes to a stop
• Key features of a displacement-time graph for a lightly damped system:
• There are many oscillations represented by a sine or cosine curve with gradually decreasing amplitude over time
• This is shown by the height of the curve decreasing in both the positive and negative displacement values
• The amplitude decreases exponentially
• The frequency of the oscillations remain constant, this means the time period of oscillations must stay the same and each peak and trough is equally spaced

#### Critical Damping

• When a critically damped oscillator is displaced from the equilibrium, it will return to rest at its equilibrium position in the shortest possible time without oscillating
• For example, car suspension systems prevent the car from oscillating after travelling over a bump in the road
• Key features of a displacement-time graph for a critically damped system:
• This system does not oscillate, meaning the displacement falls to 0 straight away
• The graph has a fast decreasing gradient when the oscillator is first displaced until it reaches the x axis
• When the oscillator reaches the equilibrium position (x = 0), the graph is a horizontal line at x = 0 for the remaining time

#### Heavy Damping

• When a heavily damped oscillator is displaced from the equilibrium, it will take a long time to return to its equilibrium position without oscillating
• The system returns to equilibrium more slowly than the critical damping case
• For example, door dampers to prevent them slamming shut
• Key features of a displacement-time graph for a heavily damped system:
• There are no oscillations. This means the displacement does not pass 0
• The graph has a slow decreasing gradient from when the oscillator is first displaced until it reaches the x axis
• The oscillator reaches the equilibrium position (x = 0) after a long period of time, after which the graph remains a horizontal line for the remaining time

#### Worked example

• Ideally, the needle should not oscillate before settling
• This means the scale should have either critical or heavy damping
• Since the scale is read straight away after a weight is applied, ideally the needle should settle as quickly as possible
• Heavy damping would mean the needle will take some time to settle on the scale
• Therefore, critical damping should be applied to the weighing scale so the needle can settle as quickly as possible to read from the scale

### 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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