C17 - Oscillations

Question 1

What’s displacement, x?

Answer 1

Distance from equilibrium position

Question 2

What’s amplitude, A?

Answer 2

Maximum displacement from eq position

Question 3

What’s a period, T?

Answer 3

Time taken to complete one full cycle

Question 4

What’s frequency, Hz?

Answer 4

Number of complete oscillations per unit time.

Question 5

What’s angular frequency, w?

Answer 5

A measure of rotation rate. (Same as angular velocity)

w = 2pif

Question 6

What’s simple harmonic motion?

Answer 6

A common oscillating motion where acceleration is directly proportional to (negative) displacement

a = - w^2 x

Where x is displacement and w is angular velocity and is a constant for the object.

Question 7

What are the key features of all objects with simple harmonic motion?

Answer 7

Acceleration of the object is directly proportional to its (negative) displacement.

The ‘-‘ means that acceleration acts in the opposite direction to displacement. It returns the object to equilibrium position.

The period, T, of the oscillator is independent of amplitude, A.

Question 8

What does the gradient of an acceleration-displacement graph for a simple harmonic oscillator show?

Answer 8

Angular frequency (-w^2)

Since the gradient for an object is constant, it’s implied that frequency is also constant.

Question 9

What’s an isochronous oscillator?

Answer 9

One where period, T (and frequency) and amplitude, A are independent.

Question 10

How is maximum velocity of an oscillator calculated?

Answer 10

v = (+/-) w√(A² - x²)

However, maximum velocity is at zero displacement therefore:

v = wA

Question 11

How does energy vary within a simple pendulum?

Answer 11

At both points of max displacement, total energy is (gravitational) potential energy.

However, as it swings, at equilibrium position total energy is kinetic.

Question 12

What does the graph for total energy within a simple pendulum oscillation look like?

Answer 12

Potential energy - looks like positive quadratic (0 at equilibrium position)

Kinetic energy - looks like negative quadratic (0 at amplitudes)

(Both overlapping)

Total energy is the sum of these two - a horizontal straight line in line with max Ep and Ek

Question 13

What’s damping?

Answer 13

When an external force acts on the oscillator, energy is lost and amplitude decreases.

Question 14

What’s light damping/when a system is underdamped?

Answer 14

When a system oscillates before stopping

Question 15

What’s critical dampening?

Answer 15

The smallest amount of dampening needed for a system not to oscillate.

Over-dampening is any dampening above this

Question 16

What’s a free oscillation?

Answer 16

When a mechanical system is displaced form its equilibrium position no then allowed to oscillate without any external forces.

Question 17

What’s a forced oscillation?

Answer 17

One in which a periodic driver force is applied to an oscillator.

The object will vibrate at the frequency of the driving force (driving frequency).

If the driving force is equal to the natural frequency, the object will resonate. (This causes the amplitude to increase greatly).

Question 18

What’s resonance?

Answer 18

When the driving frequency of a forced oscillation is equal to the natural frequency of the oscillating object.

For a forced oscillator with negligible damping, at resonance, driving frequency = natural frequency of the forces oscillator.

Question 19

What happens when an object resonates?

Answer 19

The amplitude of the oscillation increases considerably.

If the system isn’t dampened, amplitude will increase to the point that the object will fail.

Question 20

What are examples of useful effects of resonance?

Answer 20

Within clocks, musical instruments, tuning circuits (e.g. car radios) and MRI scans.

Question 21

What happens as the amount of damping increases?

Answer 21

• amplitude of vibration at any frequency decreases.
• maximum amplitude occurs at a lower frequency than fo (natural frequency).
• the peak in the graph becomes flatter and broader.