Circular Motion and SHM

Question 1

What kind of motion will a pendulum perform?

Answer 1

Simple harmonic motion

Question 2

If the graph of displacement is cos(x), what will the respective graphs of velocity and acceleration look like SHM?

Answer 2

Velocity as -sin(x)
Acceleration as -cos(x)

Same as SVA in maths for differentiating / integrating

Question 3

Describe a freely oscillating object

Answer 3

It oscillates with a constant amplitude because there is no external force acting on it

(Its energy is constant)

Question 4

What is natural frequency?

Answer 4

The frequency of free oscillations of an oscillating system.

Question 5

What are forced vibrations?

Answer 5

Making an object oscillate at a frequency that is not it’s natural frequency

Question 6

When does resonance occur?

Answer 6

When the frequency of driving force or oscillation matches the natural frequency of the system.

Question 7

What is the outcome of resonance?

Answer 7

An increase in amplitude of the system’s oscillation.

Question 8

What is damping?

Answer 8

The term used to describe the removal of energy from an oscillating system.

Question 9

What are the three levels of damping?

Answer 9

Light
Heavy
Critical

Question 10

Describe the motion of a lightly damped system

Answer 10

The system oscillates over a long time frame before coming to rest.
The amplitude of the oscillations exponentially decay. But the time period of oscillations remains constant

Question 11

Describe heavy damping (over damping)

Answer 11

System not allowed to oscillate.

Slowly returns to equilibrium.

Question 12

Describe critical damping

Answer 12

The oscillating system returns to the zero position of the oscillation after one quarter of a time period.

Question 13

What are the two conditions for SHM?

Answer 13

1. Acceleration must be proportional to displacement
2. Acceleration must be opposite to displacement

Question 14

Label up the maximum and minimum velocities and accelerations on the simple pendulum…

Answer 14

Question 15

Label up the maximum and minimum velocities and accelerations on the mass spring system…

Answer 15

Question 16

Label up the maximum and minimum potential and kinetic energies on the simple pendulum…

Answer 16

Question 17

What are the kinetic energy, potential energy and total energy lines for one cycle of SHM?

Answer 17

Question 18

When do you use?

x=Acos(wt)

When do you use?

x=Asin(wt)

Answer 18

x=Acos(wt) -> displacement in SHM when x=A when t=0

x=Asin(wt) -> displacement in SHM when x=0 when t=0

MUST BE IN RADIANS

Question 19

How do you calculate KE_max or PE_max or E_T in SHM?

Answer 19

Question 20

What two factors affect the time period of a mass spring system in SHM?

Answer 20

1. Mass on the end of the spring
2. Spring constant (stiffness) of spring

Question 21

What two factors affect the time period of a simple pendulum in SHM?

Answer 21

1. Length between top of string and centre of bob
2. Gravitational field strength

Question 22

What could the graph of energy against displacement look like in SHM?

Answer 22

Question 23

Does circular motion count as SHM?

Answer 23

When projected onto a flat surface, yes it does

Question 24

When a SHM system is lightly damped what happens to its amplitude and time period?

Answer 24

Amplitude decreases (as it loses energy)

But time period remains constant

Question 25

How is natural frequency determined for a mass spring system?

Answer 25

Question 26

How is natural frequency determined for a simple pendulum?

Answer 26

Question 27

What happens if the frequency of driving force is less than the natural frequency of a system? f>f₀

Answer 27

Low amplitude oscillations Force and system oscillate with a constant phase difference of 0

Question 28

What happens if the frequency of driving force matches the natural frequency of a system? f=f₀

Answer 28

**Resonance occurs** Large amplitude oscillations Force and system oscillate with π/2 constant phase difference

Question 29

What happens if the frequency of driving force is more than the natural frequency of a system? f\>f₀

Answer 29

Low amplitude oscillations Force and the system oscillate with a constant phase difference of π

Question 30

The graph below shows driven oscillations with varying frequencies. Add two lines if the system is: 1. Undamped (free oscillations) 2. Over damped

Answer 30

Question 31

For Barton's pendulum which two balls oscillate?

Answer 31

P and Y because they have the **same length** So **natural frequency of y matches** frequency of driving force from **P** Y resonates and its amplitude is the largest with a phase difference of π/2 compared to P

Question 32

How does the time period differ for two pendulums of different amplitudes?

Answer 32

Time period is the same for both pendulums. Time period is independent of amplitude

Question 33

What are some examples of simple harmonic motion?

Answer 33

* A pendulum * A mass bouncing on a spring * Modelling atomic bonds

Question 34

What does KE_max equal?

Answer 34

KE_max = PE_max = Total energy = ½m**ω**²A²

Question 35

How do you calculate total energy at **any** point in SHM?

Answer 35

KE + PE at that point

Question 36

When do pendulums undergo SHM?

Answer 36

When θ is small (less than 10 degrees / 1/18π radians)

Question 37

Describe damping forces and their relation to velocity

Answer 37

Damping forces always oppose motion Damping forces **∝** v² Therefore, damping forces are max at x=0 and min at x=A

Question 38

What are forced oscillations?

Answer 38

Oscillations produced by an external periodic force that has its own associated frequency

Question 39

What will happen if pendulum y on Barton's pendulum is released, in reference to the shorter pendulum x? X has a shorter length than y

Answer 39

Therefore, x has a larger natural frequency X will oscillate with a smaller amplitude and phase difference of 0 radians

Question 40

What will happen if pendulum y on Barton's pendulum is released, in reference to the longer pendulum z? Z has a greater length than y

Answer 40

z has a smaller natural frequency than y Z oscillates at a lower amplitude with phase difference π radians

Question 41

If the graph of displacement is sin(x), what will the respective graphs of velocity and acceleration look like for SHM?

Answer 41

Velocity is cos(x) Acceleration is -sin(x) Same as SVA in maths for differentiating / integrating

Question 42

What angle unit must you use for SHM?

Answer 42

Radians