Topic 4: Oscillations and waves Flashcards
Describe where KE and PE are of a mass moving between two horizontal springs
Kinetic energy: Moving mass
Potential energy: Elastic potential energy in the springs
Describe where KE and PE are of a mass moving on a vertical spring
Kinetic energy: Moving mass
Potential energy: Elastic potential energy in the springs and gravitational potential energy
Describe where KE and PE are of a simple pendulum
Kinetic energy: Moving pendulum bob
Potential energy: Gravitational potential energy of bob
Describe where KE and PE are of a buoy bouncing up and down in water
Kinetic energy: Moving buoy
Potential energy: Gravitational potential energy of buoy and water
Define: displacement (in terms of SHM).
The instantaneous distance of the moving object from its mean position in a specified direction.
Define: amplitude (in terms of SHM).
The maximum displacement from the mean position.
Define: frequency (in terms of SHM).
The number of oscillations completed per unit time.
Define: period (in terms of SHM)
The time taken for one complete oscillation.
Define: phase difference
A measure of how in phase different particles are.
When are particles said to be in phase?
If they are moving together; at 0; 360, …
What is the symbol for phase difference?
phi, ϕ
When are particles said to be completely out of phase?
at 180º or π rad
Define: simple harmonic motion
The motion that takes place when the acceleration, a, of an object is always directed towards, and is proportional to, its displacement from a fixed point. This acceleration is caused by a restoring force that must always be pointed towards the mean position and also proportional to the displacement from the mean position.
What is the defining equation for SHM?
a = -ω2 x
- ω2 is the gradient of the line
Describe the interchange between kinetic energy and potential energy during SHM
In SHM, the total energy is interchanged between kinetic energy and potential energy. If no resistive forces that dissipate energy act on the motion, the total energy is constant and the oscillation is said to be undamped.
Potential energy increases as we move away from the equilibrium position and kinetic energy decreases. As we come closer to the equilibrium position its vice versa. Potential energy can be expressed as a sine curve, kinetic energy as a cosine curve.
Define: damping
Involves a frictional force that is always in the opposite direction to the direction of motion of the oscillating particle. As the particle oscillates, it does work against this resistive (or dissipative) force and so the particle loses energy.
total energy of the particle ∝ (amplitude)<span>2</span>
This means that the amplitude decreases exponentially with time.
Define: light damping
The resistive force is small, so a small fraction of the total energy is removed with each cycle and hence the amplitude decreases. The time period of the oscillations is not affected and the oscillations continue for a significant number of cycles. The time taken for the oscillation to die out can be long.
Define: critical damping
Involves an intermediate value for a resistive force such that the time taken for the particle to return to zero displacement is a minimum. There is no overshoot.
Define: heavy damping
Involves large resistive forces and can completely prevent oscillations from taking place. The time taken for the particle to return to zero displacement can be long.
Define: natural frequency of vibration
When the system is temporarily displaced from its equilibrium position and the system oscillates as a result.
Define: forced oscillations.
It is possible to force a system to oscillate at any frequency by subjecting it to a changing force that varies with the chosen frequency. This periodic driving frequency must be provided from outside the system. When the driving frequency is first applied, a combination of natural and forced oscillations take place, producing complex transient oscillations. Once the amplitude of the transient oscillations dies down, a steady condition is achieved.
What are the conditions of forced oscillations?
- system oscillates at the driving frequency
- amplitude of the forced oscillations is fixed (each cycle, energy is dissipated as a result of damping and the driving force does not work on the system, the overall result is that the energy of the system remains constant)
- amplitude of forced oscillations depends on:
- comparative values of the natural frequency and the driving frequency
- amount of damping present in the system.
Define: resonance
Occurs when a system is subject to an oscillating force at exactly the same frequency as the natural frequency of oscillation of the system.
Describe resonance in vibrations in machinery
When in operation, the moving parts of machinery provide regular driving forces on the other sections of the machinery. If the driving frequency is equal to the natural frequency, the amplitude of a particular vibration may get dangerously high.

