SHM, Circular Motion

Question 1

[def] Period, T

Answer 1

Time taken for one complete circuit
UNIT: s

T=1/f

Question 2

[def] Frequency, f

Answer 2

Number of cycles per unit second
UNIT: Hz

f= 1/T

Question 3

[def] Radian

PUT CALCULATOR IN RAD MODE

Answer 3

a unit of measurement equal to (180/pi) degrees ~ 57.3 degrees
Equivalent to the angle subtended at the center of a circle by an arc of equal length to the radius

UNIT: rad

Question 4

[def] Angular velocity, ω

Answer 4

The rate of change of ϴ
ie the angle swept out by the radius per second

UNIT: rad s-1

ω includs word ANGULAR (instead of linear speed = v)

Question 5

Angular velocity equations (x2) simple ones!

Answer 5

ω = ϴ /t

ω = 2πf

Question 6

centripetal force

Answer 6

resultant force towards the center, acting on a body moving at constant speed in a circle

Question 7

Types of centripetal force (x4)

Answer 7

weight
tension
normal contact force
friction

Question 8

Objects in circular motion are _________ because…

Answer 8

Objects in circular motion are ACCELERATING because their direction is always changing

(Centripetal) acceleration directed towards the center

Question 9

Linear speed or velocity of an object in circular motion, v

Answer 9

TANGENTIAL to centripetal force

Question 10

Satellites in orbit explained (x3 points)

Answer 10

continually falling towards earth

weight = centripetal force

Curvature of the earth = never closer to earth

Question 11

[def] simple harmonic motion

Answer 11

SHM occurs when an object moves such that:

1. Its acceleration is always directed towards a fixed point
2. Acceleration is proportional to its distance from the fixed point

[acceleration is equal to negative ddisplacement]

Question 12

SHM acceleration equation

Answer 12

a = -(ω^2)x

Question 13

SHM Period, T, of an oscillating body

Answer 13

Time taken to complete one cycle
UNIT: s

T= 1/f = 2π/ω

Question 14

SHM Amplitude, A

Answer 14

The maximum value of the object’s displacemend from the equilibrium position

UNIT: m

Question 15

SHM T and A relationship

Answer 15

Time period (T) INDEPENDENT of amplitude (A)

Question 16

SHM pendulum: middle of swing:
v?
a?
x?

Answer 16

v= max
a = zero
x = zero

Question 17

SHM pendulum: top of one swing:
v?
a?
x?

Answer 17

v: zero
x: max (+ve)
a: max (-ve)

if x -ve, then a +ve

Question 18

[def] phase

Answer 18

the phase of an oscillation is the angle (ωt + ε) in the equation x= A cos(ωt + ε)
ε = phase constant

Question 19

Phase constant, ε

Answer 19

How much the graph is shifted.

Can calculate if other variables are known

Question 20

switch from sin graphs to cos graphs

Answer 20

cos–> (+π) –> sin
^ v
^ v
cos

Question 21

Displacement and velocity SHM equations

[given]

Answer 21

v= -Aωsin(ωt + ε)
x= A cos(ωt + ε)
sin and cos can be switched depending on starting point

Question 22

velocity SHM equation WITH AMPLITUDE

not given in data booklet

Answer 22

(v^2) = (ω^2)*(A squared - x squared)

Question 23

SHM total vibrational energy

Answer 23

Total vibrational energy=½ (m * ω^2 * A^2)

This value is constant, irrelevant to T

Question 24

SHM KE equation

Answer 24

KE= ½ m v^2
KE= ½ m (A^2 * ω^2 * sin^2(ωt))

Question 25

SHM Ep equation (potential energy)

Answer 25

Ep  =        ½ k       *        x^2
Ep =  (½ m * ω^2)*(A^2 * cos^2(ωt))

Question 26

SHM KE GPE graph: Amplitude

Answer 26

Max GPE = Min KE, same total energy

[Single parabola, GPE y=x^2, KE = sad face]
see notes
http://tap.iop.org/vibration/shm/305/page_46596.html

Question 27

SHM KE GPE graph: Total energy

Answer 27

Max GPE = Min KE, same total energy

[like cos graph sin graph because the shapes repeat]
see notes
http://www.cyberphysics.co.uk/topics/shm/shmEnergy.html

Question 28

[def] Free Oscillations [aka natural oscillations]

Answer 28

When an oscillatory system is displaced and released

• -> no external driving force once in motion
• -> frequency of free oscillations = natural frequency

Question 29

[def] Damping

Answer 29

Amplitude of free oscillations is reduced because of resistive forces

Question 30

[def] Critical Damping

and one EG

Answer 30

When the resistive forces on the system are just large enough to prevent oscillations occurring at all when the system is displaced and released

EG Vehicle suspensions: aim to quickly return to equilibrium

Question 31

Damping: X3 types

Answer 31

Light Damping: amplitude gradually reduced
Over Damping: returns to equilibrium without oscillation
Critical Damping: returns to equilibrium ASAP without oscillation

Question 32

Damping: impact on natural frequency

Answer 32

Increased damping = decreased natural frequency

THINK GRAPH:
https://i.stack.imgur.com/c0FQ1.jpg

Question 33

Light damping graph equation

A-t graph

Answer 33

x = Ao * e^(-λt) * cos(ωt + ε)

Question 34

[def] forced oscillations

Answer 34

a sinusoidally varying DRIVING FORCE is applied, causing the system to oscillate with the frequency of the applied force
[when a periodic force is applied]

Question 35

[def] resonance

Answer 35

Occurs when the periodic force equals the natural frequency

This makes the amplitude of the resulting oscillations very large

Question 36

Resonance

- + + +

Answer 36

• BAD on millennium bridge
  + GOOD for MRIs (magnetic resonance imaging)
  + GOOD for playgroud swings
  + GOOD for microwave cooking