Oscillations Flashcards
What is displacement?
It is the instantaneous distance of moving object from its means position.
What is amplitude?
It is the maximum displacement from the mean position
What is time period?
It is the time taken for one complete oscillation
What is frequency?
It is the number of oscillations per unit time
What is angular frequency (omega)?
It is the rate of change of angular displacement.
(Omega) = 2(pi)f
What is phase differences?
It is a measure of how much one wave is out of step with another wave
(Phi) = 2(pi)t/T
T is the time period and t is the time lag between the waves.
What is simple harmonic motion?
It is the acceleration proportional to the displacement and directed towards a fixed point.
What are the requirements for SHM?
- Mass that oscillates
- Position where the mass is in equilibrium
- Restoring force that acts to return mass to equilibrium
What is the formula for simple harmonic motion?
a = -(omega)^2 * x
What does the negative sign in the equation of simple harmonic motion mean?
It represents that the a and x are in opposite directions - where a is always directed towards the mean position.
What are the formulas for displacement in a simple harmonic motion?
X = Xo * sin(omega * t)
X = Xo * cos(omega * t)
What is the formula for velocity?
V = +- (omega) (Xo^2 - x^2)^1/2
V = Vo * cos (omega * t)
V = - Vo * sin (omega * t)
What is the formula for acceleration in a simple harmonic motion?
a = -(omega)^2 (x)
Can apply one of the 2 displacement equations.
What is the derivation of the formula for kinetic energy?
V = +- (omega) (Xo^2 - x^2)^1/2
Substitute into
Ek = 1/2mv^2
What is the formula for Potential energy in a simple harmonic motion?
Et = Ep + Ek
Ep = Et - Ek
Et = 1/2m(omega)^2*(x)^2
What is damping?
It is the loss of energy and reduction in amplitude from an oscillating system caused by force acting in opposite direction to the motion.
What is light damping?
System oscillates about equilibrium position with decreasing amplitude over a period of time.
What is critical damping?
The system does not oscillate & is amount of damping required such that the system returns to its equilibrium position in the shortest possible time.
What is the heavy damping?
The damping is so great that the displaced object never oscillates but returns to its equilibrium position very very slowly.
Describe and example of oscillation and its damping in a car suspension.
The car oscillates due to spring like connections at the wheels.
Critical damping is needed in order to stop oscillation as quickly as possible to avoid motion sickness - hydraulic nature.
Describe an example of oscillation in tall buildings and its oscillation.
The oscillation occurs during earthquakes.
A large weight is applied at the top of the building to supply a counter weight to counter the oscillation.
What is the natural frequency of natural frequency?
It is the unforced frequency of oscillation of a freely oscillating object.
What is free oscillation?
It is the oscillatory motion not subjected to an external periodic driving force - oscillating at natural frequency.
What is forced oscillation?
It is oscillation that is caused by an external driving force; frequency is determined by the driving force.
