Oscillations Flashcards
Period, frequency, angular frequency, displacement, amplitude, phase difference, simple harmonic motion, energy in s.h.m., damping, resonance, ultrasound
Period of an oscillation
The time taken to complete one oscillation.
Frequency
The number of oscillations per unit time.
f =
f = 1 / T
Displacement
Distance from the equilibrium position.
Amplitude
Maximum displacement.
Simple harmonic motion
Motion in which:
1) acceleration is directly proportional to its displacement from the equilibrium position
and
2) acceleration and displacement are always in opposite directions.
In s.h.m., the acceleration is always directed towards _____________.
the equilibrium position.
Angular frequency
ω = 2πf
ω = 2π / T
Where does maximum speed occur?
At the equilibrium position,
at x = 0
How do you get the equation for kinetic energy in s.h.m.?
Check notes.
Use KE = 1/2mv^2 and velocity in s.h.m. from formulae sheet.
Potential energy in s.h.m.?
Check notes.
Total energy in s.h.m.?
The total energy remains constant throughout (assuming there are no energy losses). Total energy = KE + PE or Total energy = max. KE or Total energy = max. PE
Sketch, on the same axis, the graph of KE, PE and total energy against displacement.
Check notes.
What are free oscillations?
Oscillations where there are no resistive forces acting on the oscillating system.
What is damping?
Damping happens when resistive forces cause the oscillator’s energy to be dissipated. The total energy of the oscillations decreases and the amplitude of oscillation decreases.
What is the effect of light damping?
It causes the amplitude of vibration to decrease gradually.
Check graph in notes.
What is the effect of critical damping?
It causes the displacement to be reduced to zero in the shortest time possible, without any oscillation of the object.
Check graph in notes.
What is the effect of overdamping?
It also causes an exponential reduction in displacement, but over a greater time (compared to critical damping).
Check graph in notes.
When a body undergoes free (undamped) oscillations, it vibrates at what frequency?
It vibrates at its natural frequency.
When does forced oscillations occur?
When a periodic driving force is applied to a system.
What is resonance?
When the driving frequency is equal to the natural frequency of vibration, amplitude of vibration becomes maximum.
Ultrasound may be generated and detected by __________ .
piezo-electric crystals
Explain the principles of the generation of ultrasound waves.
Ultrasonic waves are produced using a piezo-electric crystal such as quartz. A potential difference applied across the crystal causes the centres of the positive and negative charges to move. This causes the crystal to change shape. When an alternating voltage is applied, the crystal vibrates. The frequency of the alternating voltage is the same as the natural frequency of vibration of the crystal, and resonance occurs. This causes the crystal to vibrate with maximum amplitude. Because of the dimensions of the crystal, the oscillations are in the ultrasonic range. Hence, ultrasonic waves are produced in surrounding medium.
Explain the principles of the detection of ultrasound waves.
Ultrasonic transducers also function as ultrasound detectors. When an ultrasonic wave is incident on the unstressed crystal, the pressure variations causes the crystal to vibrate. An alternating potential difference is produced across the crystal. This p.d can then be amplified and processed.