Vibrations (unit 3) Flashcards
If it at equilibrium at t=0
ε= π/2
SHM?
Acceleration towards a fixed point
directly proportional to the distance from that point
Importance of critical damping in car suspension?
-return quickly to equilibrium
Resonance meaning?
-At a certain driving frequency there is a maximum in the amplitude of the oscillating load
-At this frequency the system is at resonance
Examples of resonance?
-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.
Period ?
-time taken for one complete cycle
Amplitude?
The maximum value of the object’s displacement (from its
equilibrium position).
Frequency?
-number of oscillations per second (Hz)
Free oscillations?
Free oscillations occur when an oscillatory system (such as a
mass on a spring, or a pendulum) is displaced and released
Natural frequency?
-The frequency of the free oscillations
What is damping?
-Damping is the dying away, due to resistive forces, of the
amplitude of free oscillations.
What is critical damping?
- the case when the resistive forces on the
system are just large enough to prevent oscillation
What is forced oscillations?
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.
Measurement of g with a pendulum practical?
-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
How to calculate g using pendulum?
- graph of time over length
- gradient from T = 2pi root l/g equation
-rearrange for g
Investigation of the damping of a string?
-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.
What does investigation for damping of a spring look like?
- 2 linked springs
- a mass and a pointer with a clamp stand a separate one for a meter ruler
How to show SHM in a equation?
- a = -w^2x
Displacment eq?
-x = Acos(wt + E)
What does resonance curve look like?
- mountain
- more damping broader the curve
If it at amplitude at t=0
-ε = 0
