Periodic Motion

Question 1

Which one of the following statements is true when an object performs simple harmonic
motion about a central point O?
A The acceleration is always directed away from O.
B The acceleration and velocity are always in opposite directions.
C The acceleration and the displacement from O are always in the same direction.
D The graph of acceleration against displacement is a straight line

Answer 1

D because a is directly proportional to displacement.

Question 2

What are the requirement for something to be in Simple Harmonic Motion?

Answer 2

Displacement and Acceleration are directly proportional. 𝑎 = −kx.
Displacement and Acceleration act in opposite directions. [or/and] Acceleration always acts towards the centre.

Question 3

FB: Equation for angular speed?

Answer 3

𝜔 = 2𝜋f, Where f = frequency of the oscillation.

Also : f = 1/T, Where T = time period of the oscillation.

Question 4

What does A and 𝜔 stand for in SHM equations?

Answer 4

A stands for the Amplitude (maximum displacement from equilibrium position)
𝜔 stands for the angular speed (how much it rotates around a point per second)

Question 5

What does Dampening do to the Amplitude vs. Frequency Graph?

Answer 5

Dampening reduces the max amplitude (at resonance) and also causes the resonance to happen at a lower frequency.

Question 6

How does total energy change in an undampened simple harmonic motion?

Answer 6

The total energy of the system stays constant. Potential energy and Kinetic energy change ratio but Ek + PE = K

Question 7

If given displacement a displacement vs. time graph for SHM what will a velocity/speed/acceleration time graph look like.
Displacement Graph looks like a sine graph.

Answer 7

Velo vs t: COSINE
ds/dt = v therefore if you differentiate it you will see its a cosine graph.
Speed vs t: absolute COSINE
Speed never negative, also if asked for an Ek graph you can square either speed or velo to get rough shape.
Acc vs t: negative SINE
dv/dt = a therefore we end up with an acceleration graph. Makes sense because: a is DP to - x

Question 8

What direction does the dampening force act in a dampened simple harmonic motion?

Answer 8

Opposite Direction to velocity.

Question 9

Where is the acceleration of an object in SHM at it’s lowest?

Answer 9

In SHM the acceleration at the equilibrium point = 0 because displacement is equal to 0.

Question 10

Definition for forced vibration?

Answer 10

System is made to vibrate due to the periodic external force.

Question 11

Define dampening.

Answer 11

Dampening is where an external force acts against the motion of the system (opposite to velocity) which reduces the amplitude and energy of the system over time.

Question 12

Different Types of Dampening:

• Light
• Heavy
• Critical

Answer 12

Light: Amplitude decreases to zero after a long time.
Heavy: Amplitude decreases to zero before a complete oscillation.
Critical: Amplitude decreases to zero as quickly as possible, no oscillations.

Question 13

What is the phase difference between the driving frequency and the oscillating frequency when the driving frequency equals 0?

Answer 13

Zero.

Question 14

What is a free oscillation?

Answer 14

Where an object oscillates with no transfer of energy to or from the surroundings. (independent of surroundings)

Question 15

When is the velocity of the object maximum during simple harmonic motion?

Answer 15

At the equilibrium position.

Question 16

What is the phase difference between the driving frequency and the oscillating frequency when the driving frequency tends to infinity. (goes really fast back and forward)

Answer 16

π Radians , 180 Degrees.

Question 17

What is the relationship between time period and Amplitude during simple harmonic motion?

Answer 17

Time period is independent of amplitude.