C17 - Oscillations Flashcards
What’s displacement, x?
Distance from equilibrium position
What’s amplitude, A?
Maximum displacement from eq position
What’s a period, T?
Time taken to complete one full cycle
What’s frequency, Hz?
Number of complete oscillations per unit time.
What’s angular frequency, w?
A measure of rotation rate. (Same as angular velocity)
w = 2pif
What’s simple harmonic motion?
A common oscillating motion where acceleration is directly proportional to (negative) displacement
a = - w^2 x
Where x is displacement and w is angular velocity and is a constant for the object.
What are the key features of all objects with simple harmonic motion?
Acceleration of the object is directly proportional to its (negative) displacement.
The ‘-‘ means that acceleration acts in the opposite direction to displacement. It returns the object to equilibrium position.
The period, T, of the oscillator is independent of amplitude, A.
What does the gradient of an acceleration-displacement graph for a simple harmonic oscillator show?
Angular frequency (-w^2)
Since the gradient for an object is constant, it’s implied that frequency is also constant.
What’s an isochronous oscillator?
One where period, T (and frequency) and amplitude, A are independent.
How is maximum velocity of an oscillator calculated?
v = (+/-) w√(A² - x²)
However, maximum velocity is at zero displacement therefore:
v = wA
How does energy vary within a simple pendulum?
At both points of max displacement, total energy is (gravitational) potential energy.
However, as it swings, at equilibrium position total energy is kinetic.
What does the graph for total energy within a simple pendulum oscillation look like?
Potential energy - looks like positive quadratic (0 at equilibrium position)
Kinetic energy - looks like negative quadratic (0 at amplitudes)
(Both overlapping)
Total energy is the sum of these two - a horizontal straight line in line with max Ep and Ek
What’s damping?
When an external force acts on the oscillator, energy is lost and amplitude decreases.
What’s light damping/when a system is underdamped?
When a system oscillates before stopping
What’s critical dampening?
The smallest amount of dampening needed for a system not to oscillate.
Over-dampening is any dampening above this
What’s a free oscillation?
When a mechanical system is displaced form its equilibrium position no then allowed to oscillate without any external forces.
What’s a forced oscillation?
One in which a periodic driver force is applied to an oscillator.
The object will vibrate at the frequency of the driving force (driving frequency).
If the driving force is equal to the natural frequency, the object will resonate. (This causes the amplitude to increase greatly).
What’s resonance?
When the driving frequency of a forced oscillation is equal to the natural frequency of the oscillating object.
For a forced oscillator with negligible damping, at resonance, driving frequency = natural frequency of the forces oscillator.
What happens when an object resonates?
The amplitude of the oscillation increases considerably.
If the system isn’t dampened, amplitude will increase to the point that the object will fail.
What are examples of useful effects of resonance?
Within clocks, musical instruments, tuning circuits (e.g. car radios) and MRI scans.
What happens as the amount of damping increases?
- amplitude of vibration at any frequency decreases.
- maximum amplitude occurs at a lower frequency than fo (natural frequency).
- the peak in the graph becomes flatter and broader.
