5.3 Oscillations

Question 1

Considering a spring oscillating, give the definitions of the following:
Displacement
Amplitude
Period
Frequency

Answer 1

X = distance from the equilibrium position (vector)
A = maximum displacement
Period = time taken for a complete oscillation
F = number of oscillations per second

Question 2

State the equation relating angular frequency and time period

Answer 2

W = 2pi / T
Where w = angular frequency and T = time period

Question 3

What are the conditions for SHM?

Answer 3

Acceleration must be directly proportional to displacement and in the opposite direction ( a @ -x)
Acceleration must act towards equilibrium

Question 4

What are the two main examples of systems which undergo 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

-w^2

Question 6

What is x as a function of t and w?

Answer 6

X = Acoswt or x = Asinwt where A is amplitude

Question 7

True or false: velocity is maximum when displacement is maximum

Answer 7

False - velocity is min at the A of oscillation, as the object changes directions. Velocity is maximum when the object passes through the equilibrium position

Question 8

How can you calculate the max speed using w and A?

Answer 8

vmax = wA

Question 9

What is damping?

Answer 9

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

Question 10

Explain the differences between light, heavy, and critical damping

Answer 10

Light - occurs naturally & A decreases exponentially
Heavy - amplitude decreases dramatically
Critical - stopped in as short a time as possible without overshooting equilibrium

Question 11

What is the difference between free and forced oscillations?

Answer 11

When an object oscillates w/out any 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 12

What is resonance?

Answer 12

When the driving frequency of the external force applied to an object is the same as the natural frequency of the object, resonance occurs. This is when the A of oscillation rapidly increases, and if there is no damping, the A will continue to increase until the system fails. As damping is increased, the A will decrease at all frequencies, and the max A occurs at a lower frequency

Question 13

Describe an experimental technique to investigate the resonance of an object

Answer 13

• suspend mass betw 2 springs attached to oscillation generator & use ruler parallel w/ system to record A
• inc f of generator slowly so the A increases, reaching max A when the driver f is the same as the natural f of the system (after that, inc f = dec A)
• since drag due to air damps the system, the A should not continue to increase until the point of system failure
• to inc accuracy, system can be filmed and A value recorded from video stills, as it can be difficult to determine this whilst the mass is oscillating.