Simple Harmonic motion, circular motion and oscillations

Question 1

Uniform circular motion is when

Answer 1

an object rotates at a steady speed

Question 2

f =

Answer 2

1/T

Question 3

V =

Answer 3

2piR/T

Question 4

The angular displacement of an object is given by

Answer 4

2pitf = 2pit/T

t = time
T = period of one rotation

Question 5

The angular speed, w =

Answer 5

angular displacement per second therefore

w = 2pi/T = 2fpi

Question 6

The velocity of an object moving around a circle at constant speed continually…

Answer 6

changes direction towards the centre of the circle therefore accelerates towards the centre centripetal acceleration

Question 7

The velocity of an object in uniform circular motion at any point is…

Answer 7

along the tangent to the circle at that point

Question 8

acceleration =

Answer 8

v^2 / r

Question 9

Centripetal force is

Answer 9

the resultant force on an object moving round a circle at constant speed

Question 10

F =

Answer 10

mv^2/r = mw^2

Question 11

theta =

Answer 11

2pi * f * t

Question 12

w =

Answer 12

v/r = theta/t = 2pi*f = angular speed (rad/s)

Question 13

a =

Answer 13

v^2 / r = w^2r

Question 14

T =

Answer 14

1/f

Question 15

sinX =

Answer 15

X for small angles

Question 16

w =

Answer 16

2pi / t

Question 17

Acceleration is always in opposite directions to the

Answer 17

displacement

Question 18

Simple harmonic motion =

Answer 18

oscillating motion when acceleration is proportional to the displacement in the opposite direction

Question 19

a (SHM) =

Answer 19

-kx = -(2pi f)^2x = -w^2x

Question 20

Displacement of bob at time t is x =

Answer 20

Acos(2pi * ft)

Question 21

The resultant force acting towards the equilibrium position is called the

Answer 21

restoring force

Question 22

To decrease the frequency of the spring you can

Answer 22

add extra mass

use weaker springs

Question 23

a (springs) =

Answer 23

-km/x

Question 24

T = (spring) =

Answer 24

1/f = 2pi * (m/k)^0.5 for angles less than 10 degrees

Question 25

T = (string) =

Answer 25

2pi * (L/g)^0.5 = mv^2 / L + mg

Question 26

Potential energy =

Answer 26

0,5 * spring constant * x^2 where x = distance/amplitude

Question 27

Energy changes between

Answer 27

kinetic and gravitational

Question 28

A freely oscillating object =

Answer 28

no frictional forces so constant amiplitue

Question 29

Dissipative forces are

Answer 29

The oscillations of a simple pendulum gradually die away because air resistance decreases the total energy of the system. The forces causing this decrease of amplitude are called dissipative forces because they dissipate the energy of the system to the surroundings as thermal energy.

Question 30

If dissipative forces then the motion is said to be

Answer 30

`damped

Question 31

amplitude =

Answer 31

maximum displacement from equilibrium

Question 32

Period =

Answer 32

one complete cycle

Question 33

Frequency =

Answer 33

number of cycles per second (Hz)

Question 34

Light damping =

Answer 34

Time period is independent of amplitude so each cycle takes same length of time as oscillations die away Amplitude decreases reducing by the same fraction each cycle

Question 35

Critical damping =

Answer 35

just enough to stop the system oscillating after it has been displaced and released from equilibrium.

Question 36

Heavy damping =

Answer 36

strong damping means the displaced object returns to equilibrium much more slowly than if the system is critically damped. No oscillating motion occurs

Question 37

All types of harmonic oscillators include

Answer 37

variations of kinetic and potential energy

Question 38

Energy of oscillator is proportional to

Answer 38

a^2

Question 39

motion in circular path at constant speed but varying velocity implying

Answer 39

an acceleration and therefore a force

Question 40

Rod in circular motion, when is tension max and min

Answer 40

Max: bottom of circle, T = F+W Min: top of circle, T = F-W

Question 41

Tension > weight because

Answer 41

circular motion has net force inwards so tension = F+/- W

Question 42

Damping graph, energy graph, displacement time graphs

Answer 42

a

Question 43

The simple pendulum is an example of a system that

Answer 43

oscillates with simple harmonic motion

Question 44

w for pendulum =

Answer 44

(g/l)^0.5

Question 45

Period of pendulum, T =

Answer 45

2pi / w = 2pi (L/g)^0.5

Question 46

To test for simple harmonic motion check for

Answer 46

a restoring force that acts directly proportion to the displacement which is increasing

Question 47

Mass-spring system, F = , a =, w^2 =, T =

Answer 47

``` F = -kx a = -kx/m w^2 = k/m T = 2pi (m/k)^0.5 ```

Question 48

When is tension max or min

Answer 48

The tension will be largest at the lowest point because it has to then supply the centripetal force and overcome the weight of he particle. It will be smallest at the highest point since here the weight is contributing to the centripetal force.

Question 49

For simple harmonic motion, a =

Answer 49

-kx = (-2pi*f)^2 * x = -w^2*x = -(2pi*f)^2(A)(cos2pi*ft) = -w^2 * Acos(wt) If starts at max displacement

Question 50

For simple harmonic motion, x =

Answer 50

Acos(2pi*ft) = Acos(wt) provided it starts at maximum displacement

Question 51

T =

Answer 51

1/f = 2pi / w

Question 52

For simple harmonic motion, x =

Answer 52

Asin(2pi *ft) = Asin(wt) provided it starts at equilibrium

Question 53

Vmax = | amax =

Answer 53

2pi*f*A = wA (maximum then all energy is potential (2pi*f)^2A = w^2A

Question 54

For simple harmonic motion, v =

Answer 54

+- 2pi*f*(A^2 - x^2)^0.5

Question 55

Total energy is directly proportional to

Answer 55

the amplitude squared

Question 56

Graph of how potential energy varies with displacement

Answer 56

y = x^2

Question 57

Graph of how kinetic energy varies with displacement

Answer 57

y = -x^2

Question 58

For a pendulum, T=

Answer 58

2pi*(L/g)^0.5

Question 59

For a mass-spring system, T = | f =

Answer 59

2pi*(m/k)^0.5 | 1/2pi * (k/m)^0.5

Question 60

Damping force is directly proportional to the

Answer 60

negative of velocity (opposite direction)