Oscillations Flashcards
What is simple harmonic motion?
Acceleration is proportional and opposite to displacement from its equilibrium position
What is the relationship between acceleration and displacement?
- They are always opposite in direction
- magnitude of acceleration is directly proportional to magnitude of displacement
Where is acceleration always pointing towards in SHM?
Acceleration is always pointing towards equilibrium
At equilibrium position, what is the velocity and the acceleration like?
- velocity is maximum
- acceleration is zero due to absence of restoring force
At amplitude (maximum displacement), what is the velocity and the acceleration like?
- velocity is zero
- acceleration is maximum due to largest restoring force
What is displacement in SHM?
Distance from equilibrium position
What is amplitude in SHM?
Maximum distance from equilibrium position
What is wavelength in SHM?
Distance between two successive particles that are in phase
What is period in SHM?
Time taken to complete one oscillation
What is frequency in SHM?
Number of oscillations per unit time
What is damping?
Damping is a phenomenon in which an oscillating system experiences dissipative forces that constantly remove the energy from the system, resulting in exponentially decrease of total energy and amplitude over time and slight increase in the period of oscillation
When does undamped / free oscillation occur?
When there is no external dissipative force acting on the oscillating system, hence the system continues to oscillate at constant amplitude
When does light damping occur?
When oscillating system experiences a gradual decrease in amplitude. Period increases slightly and stops oscillating after a large number of oscillations
(It experiences some external dissipative force)
What is an example of light damping?
Oscillating pendulum in air
What is external dissipative force?
Resistive force, eg. air resistance, friction
When does critical damping occur?
When system does not oscillate, instead it returns to equilibrium in the shortest time possible after being displaced
What is an example of critical damping?
Car suspension system
When does heavy damping occur?
When system does not oscillate and returns to its equilibrium after a very long time
What is an example of heavy damping?
Doors in lecture theatre
What is the difference between free and forced oscillations?
- free oscillation occurs when there is no dissipative force acting, so energy and amplitude are constant. It oscillates at its own natural frequency due to restoring force only
- forced oscillation occurs when an external periodic force is applied to a system such that energy is transferred to the system periodically/continuously, the system oscillates at the frequency of the external driver
What is the important feature about forced oscillations?
The system oscillates at the frequency of the external driver
What is resonance?
- Resonance is a phenomenon where the system achieves maximum amplitude
- It occurs when the frequency of the external driver coincide with the natural frequency of the system, maximum transference of energy from the driver to the oscillator takes place
How can resonance be avoided?
Resonance can be avoided by adjusting the forced oscillating frequency to be far from the natural frequency of the oscillating system
Why do resonance need to be avoided?
Resonance will produce maximum amplitude of oscillation and may lead to the disintegration of the oscillating system
What does the amplitude of forced oscillations depend on?
- degree of damping of the given system
- relative value of the natural frequency of the driven system and the value of frequency of the external driving force
- energy/amplitude of the periodic driving force
What happens to amplitude with varying degrees of damping when driver frequency is very low?
- very slow
- thus driver force can overcome the constant dissipative force (i.e. damping)
- amplitude of various damping is around the same
What happens to damping at high driver frequency?
At a much higher frequency than natural frequency, damping effect has a significant impact on amplitude of the oscillating system
What is oscillation?
A to-and-fro movement of a particle about a fixed point
What is frequency in SHM?
The number of cycles per unit time made by the oscillating object
What is phase?
an angle which gives a measure of the fraction of a cycle that has been completed by an oscillating particle or wave
