5.3 Oscillations

Question 1

what is the definition of displacement (in terms of oscillations)?

Answer 1

displacement is the distance an object move from its equilibrium/rest position, may be positive or negative (in metres)

Question 2

what is the definition of amplitude?

Answer 2

amplitude is the maximum displacement from the equilibrium position and will always be positive (in metre)

Question 3

what is the definition of period?

Answer 3

period is the time taken for 1 complete pattern of oscillation at any point (in seconds)

Question 4

what is the definition of frequency?

Answer 4

frequency is the number of oscillations per unit time at an point, number of cycles per second (in Hz)

Question 5

what is the definition of phase difference?

Answer 5

phase difference,Φ, is the fraction of a complete cycle or oscillation between 2 oscillating points

Question 6

what is the formula for angular frequency?

Answer 6

ω = 2π / T or ω = 2πf

Question 7

what is the difference between angular velocity and angular frequency? which applies to circular motion and which applies to oscillations?

Answer 7

they have the same formula but angular frequency is the magnitude of the vector quantity of angular velocity, they are both measure in rad s^-1 but…
angular velocity –> circular motion (vector)
angular frequency –> oscillations (scalar)

Question 8

what is the equation of simple harmonic motion?

Answer 8

a = -ω^2x
where a = acceleration
ω = angular frequency
x = displacement

Question 9

what is simple harmonic motion?

Answer 9

when an object oscillates and the acceleration of the object is directly proportional to its displacement and acts in the OPPOSITE direction to he acceleration (towards the fixed midpoint)

Question 10

what is the restoring force in oscillations (think of a pendulum)?

Answer 10

the restoring force acts in the opposite direction to the displacement (brings it back to the middle)

Question 11

how do you determine the period/frequency of a simple harmonic oscillator?

Answer 11

• to work out the frequency use 1 / T
• the best place to time from is in the middle because there is less error than recording at maximum displacement because at max displacement the velocity is slower as its changing direction and spends more time there so timing at that point increases inaccuracy
• you need to time for 10 oscillations then work out the mean and divide by 10

Question 12

in SHM, are frequency and period dependent on the amplitude?

Answer 12

no, they DO NOT depend on the amplitude

Question 13

what is an isochronous oscillator?

Answer 13

in SHM, the frequency and period are independent of the amplitude (they’re constant for a given oscillation) so a pendulum clock will keep ticking in regular time intervals even if its swing becomes very small, this kind of oscillator is called an isochronous oscillator

Question 14

when is the velocity max in a swinging pendulum?

Answer 14

at the midpoint (where x = 0) most KE

Question 15

when is the velocity 0 in a swinging pendulum?

Answer 15

when displacement is max (at the ends of the swing)

Question 16

when is the displacement max in a swinging pendulum?

Answer 16

at the ends of the swing

Question 17

when is the displacement 0 in a swinging pendulum?

Answer 17

at the midpoint, equilibrium position

Question 18

when is the acceleration max in a swinging pendulum?

Answer 18

when displacement is max (at the ends of the swing)

Question 19

when is the acceleration 0 in a swinging pendulum?

Answer 19

at the midpoint (where x = 0)

Question 20

what are the two ‘solutions’ to a = -ω^2x?

Answer 20

x = Asin(ωt) and x =Acos(ωt)

the angle must be in radians

Question 21

when should you use x = Asin(ωt)? (sine shape)

Answer 21

you should use it when you begin timing as the object passes through the midpoint where x = 0

Question 22

when should you use x =Acos(ωt)? (cos shape)

Answer 22

you should use it when you begin timing when the object is at its maximum displacement where x = max

Question 23

what is the equation for the velocity of a simple harmonic oscillator?

Answer 23

V = +- ω (A^2 - x)^0.5
where A = amplitude
ω = angular frequency
x = displacement from the rest point
the +- is present because velocity is a vector and could be in the positive or negative direction

Question 24

what is the equation for the MAX velocity of a simple harmonic oscillator? and how can you get to it from V = +- ω (A^2 - x)^0.5?

Answer 24

Vmax = +- ωA
(you can get it from making displacement (x) = 0 at max velocity using V = +- ω (A^2 - x)^0.5 which simplifies to the above equation)

Question 25

what is the equation for MAX acceleration?

Answer 25

Amax = ω^2A
where ω = angular frequency
A = amplitude
(LEARN THIS ONE)

Question 26

what does the gradient of a displacement time graph of a simple harmonic oscillator give you?

Answer 26

velocity

Question 27

what does the gradient of a velocity time graph of a simple harmonic oscillator give you?

Answer 27

acceleration

Question 28

in a swinging pendulum where is there max kinetic energy and max gravitational potential energy?

Answer 28

max kinetic energy = equilibrium/rest position

max gravitational potential energy = max displacement

Question 29

what is the mechanical energy?

Answer 29

the sum of the potential and kinetic energy is called the mechanical energy and stays constant (as long as the motion isn’t damped)

Question 30

what are the energy transfers in a vertical spring-mass system? at max displacement, equilibrium postion and at max displacement?

Answer 30

at max displacement, (when stretched fully)
KE = 0
GPE = Min
EPE = Max

equilibrium position
KE = Max
GPE = 0.5xMax
EPE = In between

at max displacement, (at the top)
KE = 0
GPE = Max
EPE = Min

Question 31

what frequency will free oscillators vibrate at?

Answer 31

their natural frequency

Question 32

what is a free oscillator?

Answer 32

an oscillator that is set into motion and has no periodic driving force acting on it, then it is described as a free oscillator

Question 33

what are forced vibrations?

Answer 33

when there is an external driving force, the frequency of this force is called the driving frequency

Question 34

what is resonance?

Answer 34

when the driving frequency is equal to the natural frequency, body will oscillate with max amplitude and at natural frequency

Question 35

what does the amplitude-frequency graph look like for natural frequency?

Answer 35

high sharp peak somewhere in the middle

Question 36

what can Barton’s pendulums highlight? (page 69)

Answer 36

demonstration of resonance, the ball with the same length of string as the driver pendulum will perform oscillations with the greatest amplitude

Question 37

what is damping?

Answer 37

damping forces reduce the amplitude of an oscillation with time, due to energy being removed from the oscillating system

Question 38

what are some real life applications of damping?

Answer 38

car shock absorbers (suspension systems of cars) to make the ride as comfortable as possible

Question 39

what is very heavy damping sometimes referred to as (can make oscillations die away)?

Answer 39

critical damping

Question 40

what are some examples of free oscillators?

Answer 40

• a pendulum swinging
• a mass-spring system
• a fishing float bobbing on the surface of water

Question 41

what are some examples of forced oscillators?

Answer 41

• a child being continually pushed on a swing
• a building vibrating during an earthquake
• the beating of a hummingbird’s wings