Module 5 Oscillations

Question 1

Define displacement and amplitude of a body.

Answer 1

Displacement is the distance travelled by a body from it’s equilibrium position.

Amplitude is the maximum displacement and is always positive in shm

Question 2

Define period.

Answer 2

It is the time taken in seconds for a body to complete one full oscillation at any point.

Question 3

Define period

Answer 3

A menstrual cycle

Question 4

Define angular frequency and phase difference.

Answer 4

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.

Question 5

When is the velocity minimum and maximum during oscillation of a body

Answer 5

Velocity is minimum during amplitude and maximum during zero displacement

Question 6

What is the relation between the resultant force and displacement for an oscillating body.

Answer 6

Resultant force is directly proportional to displacement but is always acting in opposite directions to displacement.

Question 7

Define simple harmonic motion.

Answer 7

A body performing shm has acceleration directly proportional to the displacement but the acceleration is always acting towards the equilibrium point.

Question 8

Show the requirements of shm in equation form.

Answer 8

(“a” is directly proportional to displacement but always acts towards the equilibrium point, opposite the direction of the displacement.)

a=-kx

Question 9

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

Answer 9

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

Question 10

What is the formula used to calculate maximum acceleration for a body in shm.

Answer 10

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

Question 11

What is the formula used to calculate velocity of a body in shm.
And what is the formula when body is at equilibrium.

Answer 11

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

Question 12

What equations can be used to calculate displacement from shm of a body displayed as a sine curve?

Answer 12

x = A x cos(w x t)
Or
x = A x sin(w x t)

Question 13

What equations of shm should you use at extremes of displacement and minimum displacement for manipulation of a sine curve?

Answer 13

x= Axcos(w x t) at extremes of displacements 
x= Axsin(w x t) at minimum displacement.

Question 14

In shm what quantity is isochronous and what other quantity is it independent of?

Answer 14

The time period is isochronous.

It is independent of amplitude.

Question 15

What angle is the limit for shm in a pendulum ?

Answer 15

10 degrees.

Question 16

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?

Answer 16

No it won’t

Period of a body in shm is isochronous is independent of amplitude of motion.

Question 17

What is the phase difference between acceleration and displacement graphs of shm, in radians and wave cycles?

Answer 17

Pi radians or 1/2 a wave cycle.

Question 18

For a body in shm what would a graph of acceleration against velocity look like?

Answer 18

A straight line of negative gradient passing through the origin.

Question 19

Define the interchange between kinetic energy and potential energy for a body in shm.

Answer 19

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)

Question 20

What is the sum of Ke and Pe in shm called?

Answer 20

Mechanical energy.

Question 21

If T is isochronous in shm, then what other quantity must be isochronous as well?

Answer 21

Frequency.

Question 22

What mode of angles should your calculator be set to solve equation of shm.

Answer 22

Radians instead of degrees.

Question 23

What is the phase difference between a graph of displacement and velocity in radians?

Answer 23

Pi/2 radians

Question 24

Describe the shape of energy displacement graphs for shm.

Answer 24

P.e and K.e are in antiphase and have equivalent amplitudes and frequency, with p.e at maximum at amplitude.

Question 25

What is the effect of light, heavy and critical damping on oscillations?

Answer 25

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.

Question 26

Define free and forced oscillations.

Answer 26

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.

Question 27

When does resonance occur and what happens to amplitude of oscillation?

Answer 27

When natural frequency and driving frequency are equal, resonance occurs and a body will oscillate with maximum amplitude.

Question 28

What does a graph of amplitude against driving frequency look like for resonance ?

Answer 28

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

Question 29

What does damping do to graph of resonance?

Answer 29

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.

Question 30

How do you prove one of the following equations for a mass spring system. f=k/m , f=k/m^1/2

Answer 30

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.