Simple harmonic and circular motion

Question 1

What are the criteria for SHM?

Answer 1

An object is displaced by some distance from a starting position. A restoring force acts to return the object to its starting position. The acceleration is always opposite to the direction of displacement and proportional to displacement.

Question 2

Graph of acceleration against displacement.

Answer 2

Straight line with negative gradient through origin.

Question 3

Formula for angular frequency

Answer 3

2πf

Or 2π/T

Question 4

Graph of displacement against time

Answer 4

Cos graph

Question 5

Graph of velocity against time

Answer 5

-sin graph

Question 6

Graph of acceleration against time

Answer 6

-cos graph

Question 7

When t=0 what is the displacement equal to?

Answer 7

The amplitude

Question 8

What factors determine frequency of oscillations in a mass spring system?

Answer 8

Extra mass increases inertia of system so moves slower and so frequency lower. Weaker springs reduce restoring force so acceleration and speed both less so frequency less.

Question 9

Describe energy changes during one oscillation of a mass spring system

Answer 9

Elastic potential energy to kinetic energy to gravitational potential energy to kinetic energy to elastic potential energy.

Question 10

Graph of KE against time

Answer 10

Sin wave but X axis connects troughs

Question 11

Graph of GPE against time

Answer 11

Cos graph but X axis connects troughs

Question 12

Graph of total energy against displacement

Answer 12

KE is n shape. GPE is u shape. Both touch but don’t cross X axis.

Question 13

Graph of amplitude against driving frequency

Answer 13

Volcano shape with peak at resonant frequency.

Question 14

How does damping affect amplitude against driving frequency graph?

Answer 14

Peaks are lower and move slightly left.

Question 15

When does the formula for time period apply to a pendulum?

Answer 15

When the angle is less than about 10 degrees

Question 16

Forced vibrations

Answer 16

Oscillations of a system subjected to an external periodic force.

Question 17

Free vibrations

Answer 17

Oscillations where there is no damping and no periodic force acting on the system so the amplitude is constant.

Question 18

Formula for phase difference

Answer 18

2pi x t/T

Question 19

Damping

Answer 19

Where the amplitude of an oscillating system decreases because of dissipative forces acting on the system which dissipate energy from the system to the surroundings.

Question 20

Light damping

Answer 20

Amplitude gradually decreases, reducing by the same fraction each cycle. The time period is independent of the amplitude.

Question 21

Critical damping

Answer 21

Just enough energy to stop system oscillating after it has been displaced from equilibrium and released. The system returns to equilibrium in the shortest possible time without overshooting. Example is car suspension.

Question 22

Heavy damping

Answer 22

Damping is so strong, the displaced object returns to equilibrium much more slowly than for critical damping. No oscillating motion occurs. Example is mass on spring in thick oil.

Question 23

Periodic force

Answer 23

A force that varies regularly in magnitude with a definite time period.

Question 24

Resonance

Answer 24

The amplitude of vibration of an oscillating system subjected to a periodic force is largest when the periodic force has the same frequency as the resonant frequency of the system. System vibrates such that its velocity is in phase with the periodic force.

Question 25

Resonant frequency

Answer 25

The frequency of an oscillating system in resonance.

Question 26

How does damping affect resonance?

Answer 26

Lighter damping means maximum amplitude larger and resonant frequency is closer to natural frequency of the system.

Question 27

What happens as the applied frequency becomes increasingly larger than the resonant frequency of a mass spring system?

Answer 27

Amplitude of oscillations decreases more and more, phase difference between displacement and periodic force increases from 1/2 pi to pi.

Question 28

What is the resonant frequency of a system with little or no damping?

Answer 28

It’s natural frequency.

Question 29

What is uniform circular motion?

Answer 29

Motion of an object moving at a constant speed along a circular path.

Question 30

Angular displacement

Answer 30

The angle an object in circular motion turns through. Equals 2pift or 2pit/T

Question 31

Angular speed

Answer 31

The rate of change of angular displacement of an object in circular motion.

Question 32

Why is an object in circular motion always accelerating?

Answer 32

Its velocity is continually changing direction so the velocity is changing.

Question 33

What is centripetal acceleration and why does it exist.

Answer 33

It is the acceleration of an object in circular motion towards the centre of the circle. The change in direction of its velocity is always towards the centre of the circle so is accelerating in that direction.

Question 34

Centripetal force definition and examples

Answer 34

The resultant force on an object that moves along a circular path. Acts towards centre of circle. For satellites in orbit, centripetal force is gravity. For object attached to string, centripetal force depends on tension and weight.

Question 35

Forces in circular motion: over a hill

Answer 35

The weight minus the contact force is the centripetal force. If the car’s velocity is too high, it will lose contact with the road and lose contact force.

Question 36

Forces in circular motion: roundabout

Answer 36

Centripetal force is provided by sideways force of friction. There is a limiting force of friction depending on the coefficient of friction so if velocity gets too high the car will skid.

Question 37

Forces in circular motion: banked track (eg nascar)

Answer 37

Like roundabouts only limiting velocity before skidding is higher as there is a component of the contact force acting horizontally. For no sideways friction, it is this horizontal component that is the centripetal force.

Question 38

Object in circular motion attached to string

Answer 38

Tension in string is force that changes. At object’s lowest point, tension is centripetal force plus weight. At highest point, tension is centripetal force minus weight.

Question 39

Why is a fiduciary marker placed at equilibrium position?

Answer 39

This is where the mass is moving with greatest speed so is near that point for the least time of any points so it reduces the error when judging when an oscillation is complete.

Question 40

How to find g using a pendulum

Answer 40

Vary the length of pendulum and time a number of oscillations. Use this the find the time period of one oscillation for different lengths. Use gradient of time period against root length to find g.

Question 41

How to find spring constant using mass-spring system

Answer 41

Vary mass on spring. Time a number of oscillations. Find time period for one oscillation for each mass. Use gradient of graph of time period against root mass to find spring constant.