Vibrations (unit 3)

Question 1

If it at equilibrium at t=0

Answer 1

ε= π/2

Question 2

SHM?

Answer 2

Acceleration towards a fixed point
directly proportional to the distance from that point

Question 3

Importance of critical damping in car suspension?

Answer 3

-return quickly to equilibrium

Question 4

Resonance meaning?

Answer 4

-At a certain driving frequency there is a maximum in the amplitude of the oscillating load
-At this frequency the system is at resonance

Question 5

Examples of resonance?

Answer 5

-Microwave ovens
-When the frequency of the microwaves matches the natural frequency of the vibration in the water molecules, it causes the amplitude to increase
-pushing a child on a swing.
- When the frequency of the push is the same as the natural frequency of the swing, the amplitude increases.

Question 6

Period ?

Answer 6

-time taken for one complete cycle

Question 7

Amplitude?

Answer 7

The maximum value of the object’s displacement (from its
equilibrium position).

Question 8

Frequency?

Answer 8

-number of oscillations per second (Hz)

Question 9

Free oscillations?

Answer 9

Free oscillations occur when an oscillatory system (such as a
mass on a spring, or a pendulum) is displaced and released

Question 10

Natural frequency?

Answer 10

-The frequency of the free oscillations

Question 11

What is damping?

Answer 11

-Damping is the dying away, due to resistive forces, of the
amplitude of free oscillations.

Question 12

What is critical damping?

Answer 12

• the case when the resistive forces on the
  system are just large enough to prevent oscillation

Question 13

What is forced oscillations?

Answer 13

These occur when a sinusoidally varying ‘driving’ force is
applied to an oscillatory system, causing it to oscillate with the
frequency of the applied force.

Question 14

Measurement of g with a pendulum practical?

Answer 14

-Adjust the length of the pendulum (measured from where the thread emerges from the cork/bung to the centre of the bob) by drawing the thread through the cork
-The pendulum should be given a small displacement.
-The time for a number of oscillations (a minimum of 5) should be measured and the period of 1 oscillation determined.
- The oscillations can be determined by measuring against a fixed point
- Repeat with different lengths at suitable
interval

Question 15

How to calculate g using pendulum?

Answer 15

• graph of time over length
• gradient from T = 2pi root l/g equation
  -rearrange for g

Question 16

Investigation of the damping of a string?

Answer 16

-Place the 500 g mass on the spring system and attach a pointer so its position can be easily read on the metre rule
-Displace the mass by a further 2.5 cm. Let go of the mass and
simultaneously start the stopwatch
-Let the mass oscillate continuously and measure the
new amplitude of the system every minute for the next eight minutes. Repeat this two more times and find the mean amplitude at each time
- Determine ln A for each time t and plot a graph to enable you to find λ.

Question 17

What does investigation for damping of a spring look like?

Answer 17

• 2 linked springs
• a mass and a pointer with a clamp stand a separate one for a meter ruler

Question 18

How to show SHM in a equation?

Answer 18

• a = -w^2x

Question 19

Displacment eq?

Answer 19

-x = Acos(wt + E)

Question 20

What does resonance curve look like?

Answer 20

• mountain
• more damping broader the curve

Question 21

If it at amplitude at t=0

Answer 21

-ε = 0