Further Mechanics, Thermal Physics & Gases Flashcards
Amplitude of Oscillations
- The amplitude of the oscillations is the maximum displacement of the oscillating object from equilibrium.
- If amplitude is constant and no frictional forces are present then the object is described as freely oscillating/vibrating.
Time period ( Simple harmonic motion)
The time for one complete cycle of oscillation. (starting from a start point and returning back to it)
Angular Velocity
The rate of change of angular displacement with time.
Angular Displacement
For any object in uniform circular motion, the object turns through an angle of 2π/T radians per second
Centripetal acceleration
The acceleration of an object towards the centre of a circle due to a constantly changing velocity at a tangent to the circle.
Centripetal Force
F= mv²/r / F= mω²r
The resultant force of an object in circular motion that always acts towards the centre of the circle.
How do banked tracks prevent the skidding of an object in circular motion?
- For an object travelling in a circular path, there is a centripetal force pushing the object towards the centre of the circle.
- On an a sloped/banked track, the force from the inwards push of the bank (+ any friction) can be provided by the centripetal force
- The support force ( Horizontal component ) will supply the centripetal force rather than the friction so there is no skidding
Why did the object experience a force down on itself when on a big dipper?
On a big dip at high speed you would be pushed in to your seat.
The difference between the support force on the object and it’s weight is the centripetal force
S = mv²/r +mg
Oscillating Motion
Oscillation is the motion back and forth about a fixed point in a straight line.
Define SHM
Simple Harmonic Motion is an oscillating motion caused by a force that repeatedly acts to restore a moving object to its equilibrium position.
Conditions for Simple Harmonic Motion
- The acceleration is proportional to the displacement
- The acceleration is in the opposite direction to the displacement
a = -ω²x
Resonance
When within a forced oscillation system the driving frequency is the same as the natural frequency, causing the amplitude to become large
Resonance is achieved when the phase difference between the driving oscillation and oscillating object is pi/2 ( but at the beginning of the motion the force driver and oscillator’s phase difference is 0)
at a systems natural frequency it is the most stable so the amplitude of the oscillations increase massively
Resonance can only occur when damping is small
Damping Forces
Damping forces are Fricitonal Forces oppose the motion of the oscillating body; they slow or stop simple harmonic motion from occurring.
ALL UNDAMPED OSCILLATORS ARE CLOSED SYSTEMS (energy does not enter or leave)
thus, TOTAL ENERGY = KE +GPE
Light Damping - slowly reduces amplitude of oscillations but keeps the time period almost constant.
Heavy Damping -
Critical Damping
An object in simple harmonic motion is experiencing light damping due to drag forces, what is the effect of this on the time period?
The object is now 2x in mass how is the frequency of oscillations affected?
T = 2π (L/g) ½
The amplitude of the oscillation does not affect the time period of the oscillation as it is not found in the time period equation.
mass also does not affect the time period because it is independent of the time period for the same reason.
Only things affecting time period are length of pendulum and gravitational field strength.
Equilibrium Position
Position of the lowest energy state
