Oscillations Flashcards
What are oscillations?
They are to and for motion about an equilibrium value.
Name example of dissociative forces that can stop an oscillation.
Frictional and viscous forces.
What is the displacement of an object in an oscillating system?
It is the distance and direction of the body from its rest or equilibrium position.
What is amplitude?
It is the maximum magnitude of displacement.
What is one oscillation
Physical value has passed from one side of its equilibrium value to the other side and back again to its original value.
What’s is frequency?
Number of complete oscillations per unit time.
What is angular frequency?
It is the circular representation of frequency. One complete oscillation is represented by 2π. ω=2πf
Unit: rad s-1
Relate period, frequency and angular frequency.
T = 1/f = 2π/ω
What is phase?
It is the stage of position of an oscillating system within the complete cycle of an oscillation.
How is phase expressed?
Fraction of T of as an angle where 2π is one cycle.
What is phase difference between two oscillations of the same frequency?
It is the difference between the phases in oscillations.
What is simple harmonic motion?
It is (to and fro) a motion in which the acceleration is proportional but opposite in direction to the displacement. a is directly proportional to -x
How is SHM related to circular motion?
When an object is in uniform circular motion, the vertical component is taken into consideration. Take the - of the vertical component of centripetal acceleration ω^2r because acceleration is in the opposite direction in SHM and using x(vertical component) = rsinθ obtain their vertical component of acceleration.
What is the equation for the definition of SHM?
a = -ω^2x
ω^2 = ?
Restoring force per unit displacement/ inertia = k/m
What are the equations for displacement, velocity and acceleration in terms of maximum displacement, velocity and acceleration?
x=x0sinωt
v=v0cosωt
a=-a0sinωt
Write x0, v0 and a0 in terms of r and ω where r is the radius of the circle.
x0=r
V0 = ωr
a0 = ω^2r
Express v in terms of x.
v=+_ ω(x0^2-x^2)^1/2
When x= 0, v is _____. Vice versa.
Maximum.
What are the conditions for a pendulum to be in SHM?
θ is very small so Sinθ is approximately equal to θ which is approximately equal to x/l where l is the length of the string. F on mass = -mgsinθ = -mgx/l.
ω^2 = g/T T= 2π/ω = 2π(l/g)^1/2
What is the Ek equation for a body undergoing SHM?
Ek = 1/2 mv^2 = 1/2mω^2(x0^2- x^2)
What is the equation for potential energy for SHM?
In a pendulum, Ep= 0.5mω^2x^2. (Why?)
In an energy time graph, what is the relationship between Ep and Ek?
And TE = Ep + Ek, the graph of Ek is one that an overturned Ep graph.
What is light damping?
It causes a displaces system to oscillate with gradual decreasing amplitude.
What is critical damping?
It causes a displaced system to return to rest at is equilibrium position in the shortest time possible without oscillating.
What is heavy damping?
It causes the displaced system to take a Long time to return to its equilibrium position without oscillating.
What are forced oscillations?
It is when an external periodic force, the oscillating force (at driving frequency) is applied to sustain oscillations, doing work against the dissipating forces (or to replace the energy post to dissipating forced.
What is natural frequency?
It is the frequency when a system oscillates without any external force.
Amplitude is at maximum when driving frequency is _____.
Equal to natural frequency.
For a resonance curve, degree if damping affects: the greater the damping the lower the _____.
Height and shape of the curve. Natural frequency and maximum amplitude the driving oscillation can provide.
Why is it that when the driving frequency is equal to the natural frequency, the amplitude is the highest?
Energy is most easily transferred as the driving force F is always reinforcing the restoring force of the forced oscillations ie they are in the same direction.
What are the lags depending on the frequency of the forced oscillations?
f0: -π
What is steady state?
It is when after a period of time of forced oscillations the system settles down to a state with steady amplitude a phase difference. The amplitude and phase difference is determined by the position of the driving frequency compared to the natural frequency.
What is resonance?
It is when driving frequency = natural frequency.
How can resonance cause problems for structures if not damped internally?
Oscillation occurs and if resonance frequency is reached it will cause the object to break.
What are the ways to reduce destruction by resonance?
- Increasing damping in the structure
- change shape, size, mass and mass distribution to change natural frequencies or frequency of driving oscillations.
