Oscillation

Question 1

Define displacement.

Answer 1

Distance travelled from the equilibrium position.

Question 2

Define amplitude.

Answer 2

Maximum displacement from the equilibrium position.

Question 3

Define time period.

Answer 3

Time elapsed during one complete cycle/oscillation.

Question 4

Define frequency.

Answer 4

Number of complete oscillations/cycles per unit time.

Question 5

Define angular frequency.

Answer 5

The rate of change of angular position, equal to angular velocity.

Question 6

How do we calculate angular velocity?

Answer 6

Omega = 2pif or 2*pi/T

Question 7

How might we practically measure the time period for an oscillation?

Answer 7

• Measure 10x full oscillations from equilibrium position
• Equilibrium position marked with fiducial marker
• Find avg time period

Question 8

Describe x, v and a for a pendulum halfway through its’ motion.

Answer 8

x = 0
v = max
a = 0

Question 9

Describe x, v and a for a pendulum at the amplitude of its’ motion.

Answer 9

x = max
v = 0
a = max

Question 10

What is the fundamental relationship that describes simple harmonic motion?

Answer 10

acceleration is directly proportional to displacement, and acts always toward the equilibrium position

Question 11

What equation likes acceleration and displacement in SHM?

Answer 11

a = - omega^2 * x

Question 12

Why is time period independent on the amplitude of an oscillator?

Answer 12

As amplitude rises, avg. speed also rises (as the max restoring force increases with sin theta) so time period remains constant irrespective of speed.

Question 13

What trigonometric expression describes displacement throughout a cycle in SHM?

Answer 13

x = A * cos (omega * t)
OR x = A * sin (omega * t)
depending on displacement at start position.

Question 14

How can we derive velocity and acceleration during a cycle in SHM?

Answer 14

By finding the derivative (gradient) of the displacement function (x curve)

Question 15

How can we determine V-max in SHM?

Answer 15

V-max = A*omega

Question 16

Give an equation describing velocity at a given point in SHM - HINT think squares and root

Answer 16

V = omega * sqrt (A^2 - x^2)

Question 17

Describe a restoring force.

Answer 17

The force that acts to return an object to its’ equilibrium position.

Question 18

What equation describes time period of a pendulum’s oscillation?

Answer 18

T = 2 * pi * sqrt (L/g)

Question 19

What limitations are applied to our calculations involving an oscillating pendulum?

Answer 19

We may only consider small angle oscillations and a point mass.

Question 20

What is the restoring force in a swinging pendulum?

Answer 20

The component of weight acting towards the eq. position.

Question 21

What is the restoring force in a mass-spring system?

Answer 21

The tension in the extended spring.

Question 22

What equation links angular frequency with spring constant?

Answer 22

omega = sqrt (k/m)

Question 23

What equation links time period of an oscillating mass-spring system?

Answer 23

T = 2 * pi * sqrt(m/k)

Question 24

How could we calculate the force exerted on an object as it oscillates in SHM? Think of the fundamental equation…

Answer 24

Since a = - omega^2 * x …
And f = ma…
F = - m * omega^2 * x

Question 25

When a mass of a spring is at its' amplitude when can be said about its' energy?

Answer 25

- Kinetic energy is a minimum as velocity is zero - Elastic potential energy is at it's greatest

Question 26

What is the total energy of a mass-spring system in SHM given by? Assume a closed system.

Answer 26

U = 1/2 mv^2 + 1/2 kx^2 I.e. sum of kinetic and potential energies

Question 27

How are elastic and kinetic energies of a mass-spring system related in simple terms?

Answer 27

Kinetic energy = Elastic potential (amplitude - instant displacement) Essentially... energy transferred from elastic store

Question 28

How can we calculate the kinetic energy of a mass on a spring oscillating in SHM given its' displacement and amplitude?

Answer 28

KE = 1/2 * k * (A^2 - x^2)

Question 29

Describe an energy-displacement graph depicting an object's oscillation.

Answer 29

Total energy U = constant, max KE = Min. at x=+-A, Max. at x=0 EP = Min. at x=0, Max. at x=+-A

Question 30

Why does the amplitude of an oscillation gradually decrease with time?

Answer 30

Work is done by the pendulum against drag, thus it transfers energy t the surroundings

Question 31

What can be said about the change in amplitude between peaks during a damped oscillator's motion?

Answer 31

The amplitude decreases by a constant ratio. This indicates an exponential relationship which can be expressed through the trigonometric displacement function.

Question 32

What is the difference between light and heavy damping?

Answer 32

Heavy damping causes a greater change in amplitude per oscillation

Question 33

What is critical damping?

Answer 33

The amplitude of a given oscillation decreases to zero in the minimum possible time.

Question 34

What is over-damping?

Answer 34

Amplitude of oscillation never reaches zero.

Question 35

Describe free oscillation.

Answer 35

These occur at the natural frequency of the oscillating system, defined by the time period calculated using 2*pi*sqrt(L/g) or 2*pi*sqrt(m/k) This means free oscillation runs at constant frequency

Question 36

Describe a forced oscillation.

Answer 36

The application of a period driving force causes the system to oscillate at a given frequency, the driving frequency.

Question 37

What is resonance?

Answer 37

A large amplitude oscillation that occurs when the driving frequency equals the natural frequency.

Question 38

How does damping affect resonant behaviour?

Answer 38

Greater damping- Amplitude of any oscillation decreases LA oscillation occurs at a lower driven frequency Wider peak shifted LEFT

Question 39

Why is damping a crucial aspect of the design of a bridge?

Answer 39

If a bridge oscillates, pedestrians act to match this oscillation with their movements This constitutes a driven oscillation This has driving frequency equal to natural frequency logically So a large amplitude oscillation occurs