When an object is set into oscillation without any continuous external driving force, it vibrates at its own characteristic frequency, known as its natural frequency. Over time, friction and internal resistive forces drain mechanical energy from the vibrating system, causing its amplitude to gradually diminish until it stops completely—a phenomenon called damping. However, if a periodic external force is applied to supply energy and its frequency matches the system's natural frequency, resonance occurs, causing the system to oscillate with maximum amplitude.
Compare the gradual decay of amplitude over time in a damped oscillation against the constant period, and understand the mechanism of Barton's pendulum.
The amplitude decreases continuously over time, but the period \(T\) remains constant.
Plotting only the amplitude against time shows the decay on its own: the amplitude falls from \(A_1\) to \(A_4\) over successive periods while each period keeps the same duration \(T\). The oscillation loses energy gradually and finally stops.
Pendulum \(C\) has the same length as driver pendulum \(X\), so it shares the same natural frequency and oscillates with the largest amplitude.
An oscillating system that is displaced and released without the action of external forces oscillates at its natural frequency.
Damping is the reduction in amplitude in an oscillating system due to the loss of energy. The amplitude decreases continuously over time, but the oscillating frequency and period \(T\) remain constant.
The oscillating system loses energy to overcome external friction or air resistance. A simple pendulum experiences significant external damping due to air resistance, but insignificant internal damping.
The oscillating system loses energy because of the stretching and compression of vibrating particles within the system itself. For the vibration of a spring, both external damping and internal damping occur significantly.
Damping can be overcome by applying a periodic external force to the oscillating system. The periodic force continuously transfers energy into the system to replace the energy lost to damping. When driven by an external periodic force, the system is said to be in forced oscillation.
Resonance occurs when a periodic force is applied to an oscillating system at a frequency equal to its natural frequency. During resonance, the system oscillates at its natural frequency with maximum amplitude.
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What is the difference between external damping and internal damping?
What happens to the frequency and amplitude of an oscillating system experiencing damping?
In Barton's pendulum experiment, why does pendulum \(C\) oscillate with the largest amplitude when driver pendulum \(X\) is displaced?
Damping slows down the frequency of the wave or lengthens the period of each cycle.
Damping only reduces the energy and amplitude of oscillation; the period \(T\) and frequency \(f\) remain constant until the motion stops entirely.
A bridge or tuning fork in resonance vibrates because it receives an overwhelmingly large force.
Resonance does not require a large force; it requires the frequency of the periodic force to match the natural frequency of the object, which maximizes energy transfer and builds up maximum amplitude.
Objective: Identify natural frequency, damping, forced oscillation and resonance.
1 What happens to the amplitude and frequency of a simple pendulum undergoing damping?
2 Under which condition does an oscillating system undergo resonance?
3 Damping is defined as the reduction in in an oscillating system due to the loss of energy.
4 During resonance, an oscillating system vibrates at its natural frequency with amplitude.
Drag each term to the correct description. If using a phone, tap the answer first, then tap the matching box.
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