Chapter 17 - Oscillations

Question 1

How does oscillating motion start?

Answer 1

All oscillating motion starts in an equilibrium position until a force is then applied

Question 2

What are the steps in the motion of an oscillating object?

Answer 2

Object is displaced from equilibrium position and released
It accelerates towards equilibrium
It slows past the equilibrium till it reaches maximum positive displacement
Accelerates to equilibrium and slows and stops at maximum negative displacement

Question 3

What is displacement?

Answer 3

The distance from equilibrium position

Question 4

What is the amplitude?

Answer 4

Maximum displacement

Question 5

What is the time period?

Answer 5

Time taken for one full oscillation

Question 6

What is the frequency?

Answer 6

Number of complete oscillations per unit of time

Question 7

What is the phase difference in oscillating objects?

Answer 7

Differences in displacement between two oscillating objects

Question 8

What does it mean when oscillating objects are in phase?

Answer 8

The identical pendulums both reach maximum positive displacement at the same time

Question 9

What does it mean when oscillating objects are antiphase?

Answer 9

One reaches its positive maximum whereas the other reaches the negative maximum

Question 10

What is angular frequency?

Answer 10

Angular frequency describes object motion closely related to angular velocity in circular motion

Question 11

What is the formula for angular frequency?

Answer 11

w = 2pi / T
w = 2fpi
w = sqrt( k / m ) for a spring
w = sqrt( g / L ) for a pendulum

Question 12

What is special about frequency in SHM?

Answer 12

Frequency of the oscillator is constant due to how ‘w²’ is a constant for the object

Question 13

What is special about period and amplitude in SHM?

Answer 13

They are independent
When amplitude increases, average speed increases
This type of oscillator is known as isochronous

Question 14

How can you show amplitude is independent to period?

Answer 14

Time oscillations of a given amount at varying amplitudes using a stopwatch or by taking the time for multiple oscillations to attain an average result

Question 15

What is a fiducial marker?

Answer 15

A reference point which could be used to show the equilibrium position for future iterations of an experiment

Question 16

What are the relationships of acceleration in SHM and displacement?

Answer 16

Acceleration is directly proportional to displacement
Acceleration acts opposite to displacement

Question 17

What is the acceleration formulas for SHM?

Answer 17

a = - c² * x
a = - (2fpi)² * x

Question 18

Why is the constant squared in the acceleration formula for SHM?

Answer 18

The square is used to preserve the negative sign by keeping the constant positive

Question 19

What does the graph of displacement against time look like typically?

Answer 19

Cosine shaped
When released from a point of maximum displacement, time is 0, and it passed zero displacement at T/4

Question 20

What does the graph of velocity time graph look like?

Answer 20

Gradient of a displacement time graph is the velocity
At maximum displacement, velocity is 0
Therefore the graph has a sine shape

Question 21

What does the graph of acceleration against time look like?

Answer 21

It is an inverted displacement time graph as it is the gradient of the velocity-time graph
Acceleration is directly proportional to the negative of the displacement so max at amplitude

Question 22

What are the formulas for displacement involving cosine and sine?

Answer 22

X = Acos(wt)
X = Asin(wt)

Question 23

How do you know whether to use the sine or cosine equation for displacement?

Answer 23

The equation is dependant on where the oscillating object is at t=0

Question 24

What is the formula for velocity at a given displacement?

Answer 24

V = +-w * Sqrt(A² - x²)

Question 25

What is the formula for the maximum velocity in a system?

Answer 25

V_MAX = (Angular Frequency)(Amplitude)

Question 26

How does total energy behave in SHM?

Answer 26

Total energy remains constant and transfers continually between KE and a form of PE as there are no external forces to transfer energy out of the system

Question 27

How does energy oscillate in a mass-spring system on a horizontal track?

Answer 27

This occurs in the horizontal plane and so GPE is constant Energy transfers between KE and EPE

Question 28

How does energy oscillate in a pendulum?

Answer 28

The string is taught so EPE is constant Energy transfers from KE to GPE as oscillation is in vertical plane

Question 29

What is the formula for kinetic energy at a point in time in SHM?

Answer 29

E_K = E_T - E_P E_K = 1/2 * k * (A² - x²)

Question 30

What is the formula for velocity in SHM?

Answer 30

v = Sqrt( k/m * (A² - x²))

Question 31

What does the graph of energy displacement look like?

Answer 31

E_K is parabolic and has max at 0 displacement E_P is parabolic and has min at 0 displacement They both have same min and max of 0 and total energy respectively

Question 32

What is dampening?

Answer 32

When an external force that acts on an oscillator has the effect of reducing the amplitude of its oscillations

Question 33

What is light damping?

Answer 33

When forces are small, the amplitude gradually decreases but the period of oscillations is almost unchanged

Question 34

What is heavy damping?

Answer 34

Larger damping forces cause amplitude to significantly decrease and the period to increase slightly

Question 35

What is free oscillation?

Answer 35

When a mechanical system is displaced from equilibrium and then allowed to oscillate without external forces

Question 36

What is the natural frequency?

Answer 36

The frequency of the free oscillations

Question 37

What is a forced oscillation?

Answer 37

One in which a periodic driver force is applied to an oscillator

Question 38

What is the driving frequency?

Answer 38

The object will vibrate at the frequency of the driving force (driving frequency)

Question 39

When does an object resonate

Answer 39

When the driving frequency of a forced oscillation is equal to the natural frequency of the oscillating object

Question 40

What happens when an object resonates?

Answer 40

Amplitude of oscillation increases until where the object fails if the system is dampened The greatest transfer of energy from driver to oscillator is at resonant frequency

Question 41

How does light damping affect resonance?

Answer 41

The maximum amplitude occurs at the natural frequency of the forced oscillator

Question 42

What changes to resonance as the amount of damping increases?

Answer 42

Amplitude of vibration at any frequency decreases Maximum amplitude occurs at lower frequency than natural Peak on graph becomes flatter and broader

Question 43

What is the formula for natural frequency?

Answer 43

f = 1/2pi * sqrt(k/m) Where sqrt(k/m) = w

Question 44

What is the method to investigate a simple pendulum?

Answer 44

Attach ball bearing to string of 'l' and clamp stand Wait till pendulum bob stops then place fiducial marker Pull bob and let go with small amplitude Count time for 10 oscillations Reduce 'l' and measure 't' Graph T² against 'l' m = 4pi²/g

Question 45

What is the method to investigate a mass-spring system?

Answer 45

Attach spring to clamp stand and attach mass holder Wait till stops moving and put fiducial marker Pull spring down and time 10 oscillations Add mass and measure time at intervals Graph T² against 'm' m = 4pi²/k

Question 46

What is the method to observe forced and damped oscillations?

Answer 46

Set up vibration generator on spring with mass holder on clamp stand above position sensor Measure distance to bottom of mass holder from position sensor Use position sensor to record maximum amplitude Increase frequency by intervals Graph amplitude against frequency