Simple harmonic motion

Question 1

Characteristics of SHM

Answer 1

Object oscillates to and fro, either side of a midpoint
There is always a restoring force pulling or pushing the object back towards the midpoint

Question 2

Condition for SHM

Answer 2

a is directly proportional to -x
a is always towards the midpoint and in the opposite direction to displacement

Question 3

how is the v-t graph related to the x-t graph

Answer 3

v-t graph is the gradient function of the x-t graph, it is a quarter of a cycle in front of the displacement

Question 4

how is the a-t graph related to the v-t graph

Answer 4

gradient function, quarter of a cycle in front of velocity

Question 5

what condition is required for the equation of the pendulum to apply?

Answer 5

amplitude of oscillation must be small (as angle must be small)

Question 6

Explain the energy changes of a pendulum undergoing SHM, starting from max displacement

Answer 6

Gravitational potential -> Kinetic -> Gravitational potential

Question 7

Describe the energy changes for a vertical mass-spring system undergoing SHM starting from max displacement

Answer 7

Elastic potential -> kinetic -> gravitational potential -> kinetic -> elastic potential

Question 8

how does total energy change over time for a system in SHM

Answer 8

For a free oscillator, total energy is sum of Ek and Ep and is always the same

Question 9

What is the effect of damping on oscillations?

Answer 9

Damping happens when energy is lost to the surroundings. Damping reduces the amplitude over time

Question 10

What is critical damping?

Answer 10

Critical damping reduces the amplitude (stops the system from oscillating) in the shortest possible time

Question 11

What is overdamping?

Answer 11

Where a system takes longer to return to equilibrium than a critically damped system.

Question 12

What are free vibrations?

Answer 12

Where an object oscillates at its resonant frequency,
There is no force acting other than internal force

Question 12

What are forced vibrations?

Answer 12

A system is forced to vibrate by a periodic external force
The frequency of this force is called the driving frequency

Question 13

What is resonance?

Answer 13

When driving frequency= resonant (natural) frequency. The system gains more and more energy from the driving force and so vibrates with a rapidly increasing amplitude
Only occurs if driving frequency is pi/2 out of phase with the oscillator

Question 14

How does damping affect resonance?

Answer 14

Lightly damped system have a very sharp resonance peak, their amplitude only increases dramatically when the driving frequency is very close to the natural frequency
Heavily damped systems have a flatter response, their amplitude doesn’t increase as much near the natural frequency and they aren’t as sensitive to the driving frequency

Question 15

Examples of the effects of damping on mechanical systems

Answer 15

Tapei 101 uses a giant pendulum to damp oscillation caused by strong winds

Question 16

Explain how damping is used to improve sound quality in enclosed spaces

Answer 16

Sound waves reflect off of the walls of the room, and stationary sound waves are formed at certain frequencies
This creates resonance, and some frequencies are louder than others
Soundproofing is a form of damping, absorbing the sound energy and converting it to heat energy

Question 17

What effect does light damping have?

Answer 17

Reduces amplitude but not time period (for a while)

Question 18

What effect does heavy damping have?

Answer 18

Reduces amplitude and quickly reduces time period