Module 5 Oscillations Flashcards
Define displacement and amplitude of a body.
Displacement is the distance travelled by a body from it’s equilibrium position.
Amplitude is the maximum displacement and is always positive in shm
Define period.
It is the time taken in seconds for a body to complete one full oscillation at any point.
Define period
A menstrual cycle
Define angular frequency and phase difference.
Angular frequency is rate of change of phase or the product of 2pi w f
Phase difference is the difference in cycle of oscillation, measured in degrees or radians.
When is the velocity minimum and maximum during oscillation of a body
Velocity is minimum during amplitude and maximum during zero displacement
What is the relation between the resultant force and displacement for an oscillating body.
Resultant force is directly proportional to displacement but is always acting in opposite directions to displacement.
Define simple harmonic motion.
A body performing shm has acceleration directly proportional to the displacement but the acceleration is always acting towards the equilibrium point.
Show the requirements of shm in equation form.
(“a” is directly proportional to displacement but always acts towards the equilibrium point, opposite the direction of the displacement.)
a=-kx
What is the constant in the equation defining simple harmonic motion?
Hence write the 3 ways in which you can write the equation for shm
In a=-kx, the constant k= w^2
So the equation can be written as
a=-w^2x or a=-(2pi/t)^2 x or a=-(2pi f)^2x
What is the formula used to calculate maximum acceleration for a body in shm.
a max=-w^2 x Amplitude
As a is directly proportional to x, so a is maximum when x is maximum and that is Amplitude
What is the formula used to calculate velocity of a body in shm.
And what is the formula when body is at equilibrium.
v=+- w x (A^2 - x^2)^1/2
At equilibrium x=0, so
v=+- w x(A^2- 0^2)^1/2
v=+- w x(A^2)^1/2
v=+- w x A
What equations can be used to calculate displacement from shm of a body displayed as a sine curve?
x = A x cos(w x t)
Or
x = A x sin(w x t)
What equations of shm should you use at extremes of displacement and minimum displacement for manipulation of a sine curve?
x= Axcos(w x t) at extremes of displacements x= Axsin(w x t) at minimum displacement.
In shm what quantity is isochronous and what other quantity is it independent of?
The time period is isochronous.
It is independent of amplitude.
What angle is the limit for shm in a pendulum ?
10 degrees.
For a pendulum with angle displaced to the horizontal less than 10 degrees, will an increase in initial displacement at which the bob is released make a difference to the time period?
Why?
No it won’t
Period of a body in shm is isochronous is independent of amplitude of motion.
What is the phase difference between acceleration and displacement graphs of shm, in radians and wave cycles?
Pi radians or 1/2 a wave cycle.
For a body in shm what would a graph of acceleration against velocity look like?
A straight line of negative gradient passing through the origin.
Define the interchange between kinetic energy and potential energy for a body in shm.
The kinetic energy is zero when the potential energy is maximum, at amplitude and the kinetic energy is maximum when potential energy is zero, at equilibrium (zero displacement)
What is the sum of Ke and Pe in shm called?
Mechanical energy.
If T is isochronous in shm, then what other quantity must be isochronous as well?
Frequency.
What mode of angles should your calculator be set to solve equation of shm.
Radians instead of degrees.
What is the phase difference between a graph of displacement and velocity in radians?
Pi/2 radians
Describe the shape of energy displacement graphs for shm.
P.e and K.e are in antiphase and have equivalent amplitudes and frequency, with p.e at maximum at amplitude.
What is the effect of light, heavy and critical damping on oscillations?
In light damping the period of oscillation is mostly unchanged but the amplitude decreases gradually.
In heavy damping the period increases a little bit and the amplitude fades faster.
In critical damping, the body is brought to rest before one complete oscillation.
Define free and forced oscillations.
Oscillations oscillating at natural frequency with no external force acting on them are free oscillations
Oscillations oscillating at the same frequency as a driving force with the driving force making a body oscillate are forced oscillations.
When does resonance occur and what happens to amplitude of oscillation?
When natural frequency and driving frequency are equal, resonance occurs and a body will oscillate with maximum amplitude.
What does a graph of amplitude against driving frequency look like for resonance ?
The graph increases gradient, with a sharp spike in amplitude at the point where resonance occurs. Then the gradient falls sharply, almost forming an inverted v but the amplitude of oscillation after resonance is higher than amplitude before resonance
What does damping do to graph of resonance?
It flattens the peak and lowers the point where resonance occurs on the x axis.
As damping increases the graph is flattened and point of resonance is shifted furthermore.
How do you prove one of the following equations for a mass spring system. f=k/m , f=k/m^1/2
Measure values for f and m by varying m.
Plot a graph of f against 1/m and f against 1/m^1/2.
The graph with a straight line through the gradient will show the correct equation.
