Simple harmonic motion unit 4

Question 1

how is angular velocity found? what are the units?

Answer 1

angular displacement / time. The units are radians/seconds.

Question 2

what is the symbol for angular velocity?

Answer 2

ω

Question 3

What is angular displacement measured in?

Answer 3

a number of π

Question 4

The end of a piece of string rotates 5 times a second. The string is 50cm long. Find the linear speed.

Answer 4

1 revolution is 2π radians. Thus angular speed is 10π radians a second.
10π * 0.5=5π

Question 5

What is the equation linking linear velocity, radius and angular velocity?

Answer 5

V=rω

Question 6

What is frequency?

Answer 6

The number of revolutions per second.

Question 7

What is the period?

Answer 7

time for 1 complete revolution.

Question 8

Why does centripetal acceleration happen?

Answer 8

It happens due to a change in direction of motion even if it moves at constant speed.

Question 9

What is centripetal force occur?

Answer 9

The resultant force on an object that makes an object move round a circular path. The force acts in the same direction as centripetal acceleration towards the center of the circle.

Question 10

When swinging a mass on a vertical string, when is it more likely to break?

Answer 10

At the bottom. This is because the tension has to be equal to that of the sum of the centripetal force and gravity.

Question 11

When swinging a mass on a vertical string, how is the tension found at the top, bottom and side?

Answer 11

At top centripetal force minus mg.
At the side just the centripetal force.
At the bottom centripetal force plus mg.

Question 12

What is simple harmonic motion?

Answer 12

An oscillation in which the acceleration of an object is directly proportional to its displacement from the midpoint and its directed towards the midpoint.
The time period is independent of the amplitude meaning it is isochronic.

Question 13

What is the phase difference between a displacement and velocity time graph of an object showing SHM?

Answer 13

π/2.

The phase difference between velocity and acceleration is also π/2.

Question 14

What is light or heavy damping?

Answer 14

Light. Will only lose a small amount of amplitude each time.

Heavy. Loses more amplitude each time.

Question 15

What happens with damping?

Answer 15

Amplitude decays over multiple periods.
The period is not affected by damping.
It is exponential decay meaning the bigger the displacement, the bigger the decrease. One peak may be 0.8 times the last one and they always increase by a factor of 0.8

Question 16

What is free oscillation?

Answer 16

Once displaced a system will oscillate at it’s natural frequency.

Question 17

How does periodic driving force work?

Answer 17

It is applied to a system to make it oscillate. The frequency of the driving period force is equal to the natural frequency of the system.

Question 18

Why doesn’t the amplitude increase to infinity with resonce?

Answer 18

Because damping will limit it.

Question 19

What is conservation of momentum?

Answer 19

For a system of interacting species, the total momentum is constant, provided no external forces act.

Question 20

what are the units for angular velocity?

Answer 20

radians per second.

Question 21

In simple harmonic motion, how is displacement measured?

Answer 21

The distance from the midpoint to the object.

Question 22

What is the restoring force in simple harmonic motion?

Answer 22

The force that always pulls or pushes the object to the midpoint.

Question 23

What affects the size of the restoring force?

Answer 23

the displacement. The greater the displacement, the greater the force.

Question 24

What provides the restoring force in a pendulum or in a mass on a spring?

Answer 24

gravity or elastic potential energy.

Question 25

In SHM, what does the restoring force do to the object when moving towards and away from the midpoint ?

Answer 25

It does work to it, and transfers PE to KE when going towards it. When going away, KE to PE.

Question 26

when is KE at a maximum?

Answer 26

At the midpoint.

Question 27

When is PE at a maximum?

Answer 27

At maximum displacement.

Question 28

What is the mechanical energy?

Answer 28

The sum of the kinetic and potential energy. It stays constant unless there is damping.

Question 29

what is the phase relationship between an acceleration and displacement time graph?

Answer 29

They are in anti phase.

Question 30

What is a cycle in SHM

Answer 30

maximum positive displacement to maximum negative displacement and back.

Question 31

is the period related to the amplitude?

Answer 31

No. This means that even if a pendulum swings become very small, they will still take the same time.

Question 32

In the max accleration equation, what does the capital A mean?

Answer 32

the maximum displacement.

Question 33

When a mass it attached to a horizontal spring and is moving around, how is the force calculated?

Answer 33

F=-kx | k is the spring constant. x is the displacement.

Question 34

When does the pendulum show SHM?

Answer 34

Only with small oscillations. Up to about 10 degrees from the midpoint.

Question 35

What is the natural frequency?

Answer 35

the frequency something oscillates at when left to its own devices.

Question 36

What happens at resonance?

Answer 36

the phase difference between the driver and the oscillator is 90.

Question 37

what is the phase relationship between the driving frequency and natural frequency ?

Answer 37

When the driving frequency is less than the natural frequency, they are in phase. When it is faster there are completely out of phase.

Question 38

when does resonance happen?

Answer 38

driving frequency = natural frequency.

Question 39

When the frequency approaches resonance and goes past resonance, what happens to the amplitude?

Answer 39

It gets larger and then falls.

Question 40

how does the damping affect the way in which resonance is reached?

Answer 40

If something is lightly damped, the amplitude will only increase when the driving frequency is close to the natural frequency and it will increase by a large amount. With heavy damping, it isn't as sensitive to the driving frequency and it doesn't increase by as much.

Question 41

what is the phase difference between a graph of particle velocity and particle displacement?

Answer 41

0.5pi

Question 42

If you add mass to a pendulum, what happens to the damping ?

Answer 42

It will have more kinetic energy when oscillating and will lose about the same amount due to air resistance than without the mass so it is less heavily damped as a smaller proportion is lost

Question 43

What are forced vibrations?

Answer 43

The driver forces the system to vibrate. If the driving frequency is less than the natural frequency they are in phase If the driving frequency is greater than the natural frequency, they are completely out of phase.