Simple Harmonic Motion

Question 1

What is simple harmonic motion?

Answer 1

The motion of an object whose acceleration is proportional to its distance from a fixed point with this acceleration always being directed towards that point.

Question 2

How is the displacement from the point of equilibrium calculated?

Answer 2

x = Acosωt

Question 3

How is velocity at a given time calculated?

Answer 3

v = -ωAsinωt

Question 4

How is the acceleration towards the point of equilibrium calculated?

Answer 4

a = -ω^2Acosωt

Question 5

How is velocity at a displacement calculated?

Answer 5

v = ±ω√(A^2-x^2)

Question 6

How is maximum velocity calculated?

Answer 6

Vmax = ±ωA

Question 7

When does the maximum velocity occur?

Answer 7

At the equilibrium position

Question 8

When does the minimum velocity occur?

Answer 8

At the maximum displacement

Question 9

How is maximum acceleration calculated?

Answer 9

a_max = -ω^2A

Question 10

When does the maximum acceleration occur?

Answer 10

When x = A, at maximum displacement

Question 11

When does the minimum acceleration occur?

Answer 11

At the equilibrium position

Question 12

How is time period calculated?

Answer 12

T = 2π/ω

Question 13

How is frequency calculated?

Answer 13

f = 1/T

Question 14

What is ω equal to?

Answer 14

2πf

Question 15

When is the minus sign in an equation ignored?

Answer 15

When asked for the magnitude

Question 16

What does the gradient of a displacement vs time graph give?

Answer 16

Velocity

Question 17

What does the gradient of a velocity vs time graph give?

Answer 17

Acceleration

Question 18

What function does a displacement vs time graph show?

Answer 18

Cosine

Question 19

What function does a velocity vs time graph show?

Answer 19

-Sine

Question 20

What function does an acceleration vs time graph show?

Answer 20

-Cosine

Question 21

What does an acceleration vs displacement graph show?

Answer 21

A straight line with a negative gradient

Question 22

How is the resulting force of a pendulum calculated?

Answer 22

F = -mgsinθ

Question 23

What is the acceleration of a pendulum?

Answer 23

a = -gsinθ

Question 24

How is the time period of a pendulum calculated?

Answer 24

T = 2π√(l/g)

Question 25

When does sinθ = θ?

Answer 25

When the angle is small and θ is in radians.

Question 26

How is the maximum velocity of a pendulum calculated?

Answer 26

Vmax = ±A√(g/l)

Question 27

How is the maximum acceleration of a pendulum calculated?

Answer 27

a_max = -(g/l)A

Question 28

How is the velocity of a pendulum calculated?

Answer 28

v = ±(√[g/l])(√[A^2-x^2])

Question 29

What is the restoring force of a spring?

Answer 29

-kx provided Hooke's Law applies

Question 30

How is the acceleration of an oscillating spring calculated?

Answer 30

a = -(k/m)x

Question 31

How is the time period of an oscillating spring calculated?

Answer 31

T = 2π√(m/k)

Question 32

How can the spring constant of an oscillating spring be found?

Answer 32

k = 4π^2 / gradient

Question 33

How is the frequency of an oscillating spring calculated?

Answer 33

f = (1/2π)(√[k/m])

Question 34

How is the maximum velocity of an oscillating spring calculated?

Answer 34

Vmax = ±(√[k/m])A

Question 35

How is the total energy of an oscillating system calculated?

Answer 35

0.5(mω^2)A^2 or 2mπ^2f^2A^2

Question 36

How can k be calculated in a system with two springs?

Answer 36

k = F/x

Question 37

How can the total energy in an oscillating spring system be calculated?

Answer 37

0.5kA^2

Question 38

What is an undamped system?

Answer 38

An SHM system in which no energy is lost.

Question 39

How does the amplitude of an undampened system change?

Answer 39

The amplitude is constant.

Question 40

What is a damped system?

Answer 40

An SHM system in which energy is lost to the surroundings

Question 41

How does the amplitude of a damped system change?

Answer 41

The amplitude decreases with time.

Question 42

What is a lightly damped system?

Answer 42

A system in which it takes many oscillation cycles before the amplitude falls to zero.

Question 43

What is a heavily damped system?

Answer 43

A system in which it the oscillations decay to zero after a few oscillations?

Question 44

What is an over damped system?

Answer 44

A system which will not oscillate.

Question 45

What is a critically damped system?

Answer 45

A system which will return to the equilibrium position in less than a quarter of the periodic time.

Question 46

What are free oscillations?

Answer 46

SHM with a constant amplitude and time period where there is no energy transfer.

Question 47

What are damped oscillations?

Answer 47

SHM in which the amplitude decreases due to damping forces in which energy is transferred to the surroundings.

Question 48

What are forced oscillations?

Answer 48

SHM that is driven by an external influence.

Question 49

What is resonance?

Answer 49

When one oscillating system is coupled to and producing forced oscillations in a second oscillating system.

Question 50

What is the natural frequency of a system?

Answer 50

The frequency at which a system oscillates when not subjected to a continuous or repeated external force.

Question 51

When is a responder resonating?

Answer 51

When the frequency of the driver matches the natural frequency of the responder.

Question 52

What is the phase difference between a responder and driver when there is resonance?

Answer 52

π/2

Question 53

What is the phase difference between a responder and driver when the driver is below the responder's natural frequency?

Answer 53

~0

Question 54

What is the phase difference between a responder and driver when the driver is above the responder's natural frequency?

Answer 54

~π

Question 55

How can the effects of resonance be decreased?

Answer 55

Damping

Question 56

Describe how simple harmonic motion in a spring can be shown experimentally.

Answer 56

- Assemble a clamp and stand on a workbench. - Attach a spring with an IR position sensor alongside a metre rule. - Add masses to the spring then pull the assembly down a set amount giving the initial amplitude. - The masses will now oscillate in SHM as will be shown by the output of the position sensor.

Question 57

How does damping affect resonance?

Answer 57

- Lightly damped systems will have a sharp resonance peak. | - Heavily damped systems are less sensitive to the driving frequency.