Oscillations PMT

Question 1

Considering a spring oscillating, give the definitions of the following:

• Displacement
• Amplitude
• Period
• frequency

Answer 1

Displacement
-distance from the equilibrium position 
Amplitude
-Maximum displacement
Period
-time taken for a complete oscillation
Frequency
- number of oscillations per second

Question 2

state the equation relating angular frequency and time period

Answer 2

ω=2pi/T

Question 3

what are the conditions for simple harmonic motion?

Answer 3

• Acceleration must be directly proportional to displacement and in the opposite direction
• It must act towards equilibrium

Question 4

what are the two main examples of systems which under go SHM

Answer 4

1. A mass spring system

2. A pendulum

Question 5

what is the constant of proportionality linking acceleration and displacement?

Answer 5

-ω^2

Question 6

what is x as a function of t and ω

Answer 6

x=Acosωt or x=Asinωt

where A is amplitude

Question 7

true or false: velocity is maximum when displacement is maximum.

Answer 7

false
the velocity is minimum at the amplitude of oscillation, as the object changes direction.
Velocity is maximum when the object passes through the equilibrium position.

Question 8

how can you calculate the maximum speed using ω and A?

Answer 8

v=ωA

Question 9

what is damping?

Answer 9

damping is the process by which the amplitude of the oscillations decrease over time. this is due to energy loss to resistive forces such as drag or friction

Question 10

define light damping

Answer 10

Light damping occurs naturally (e.g. pendulum oscillating in air), and the amplitude decreases exponentially (but time period remains constant as A and T are independent)

Question 11

define heavy damping

Answer 11

Heavy damping occurs when the resistive forces acting are large – not even one complete oscillation occurs as the system slowly returns to equilibrium.

Question 12

define critical damping

Answer 12

in critical damping the object is stopped in as short a time as possible without over shooting equilibrium

Question 13

What is the difference between free and forced oscillations?

Answer 13

when an object oscillates without ant external forces being applied, it oscillates at its natural frequency. this is known as free oscillation. Forced oscillation occurs when a periodic driving force is applied to an object, which causes it to oscillate at a particular frequency.

Question 14

What is resonance?

Answer 14

when the driving frequency of the external force applied to an object, resonance occurs. this is when the amplitude of oscillation rapidly increases, and if there is no damping, the amplitude will continue to increase until the system fails. As damping is increased, the amplitude will decrease at all frequencies, and the maximum amplitude occurs at a lower frequency.

Question 15

describe an experimental technique to investigate the resonance of an object

Answer 15

• suspend a mass between two springs attached to an oscillation generator and use a ruler parallel with the spring mass system to record the amplitude.
• Increase the frequency of the generator slowly so that the amplitude increases, reaching maximum amplitude when the driver frequency is the same as the natural frequency of the system (after which, increasing the frequency will decrease the amplitude)
• since drag force due to the air damps the system, the amplitude should not continue to increase until the point of system failure.
• To increase accuracy, the system can be filmed and the amplitude value recorded from video stills, as it can be difficult to determine this whilst the mass is oscillating.