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Physics Oscillations
Physics Autumn Y13
| Question | Answer |
|---|---|
| Definition of SHM | Motion such that acceleration is directly proportional to displacement and always acts towards equilibrium (a proportional to -x) |
| Proof for a = A w^2 | Circle. radius = A. a = centripetal acceleration. theta = angle to x axis At any time t, theta = w x t (rads and seconds) v = r w = A w a = w^2 r = A w^2 a = A w^2 |
| For physics | USE RADIANS FOR THE LOVE OF GOD DANIEL LIKE LITERALLY FOR EVERYTHING MOST OF THE EQUATIONS DONT WORK IF YOU USE DEGREES |
| Proofs for displacement, velocity and acceleration of oscillations | Consider the circle thing. Project onto x axis. x = A costheta. theta = wt dy/dx so Vx = -vsin theta = -Aw sin(wt) ax = -a costheta = -A w^2 cost(wt) |
| a proportional to -x | Constant of proportionality is w^2 |
| Proof for the velocity of oscillations formula in booklet | v = -Aw sin(wt) Square both sides make the sin^2(wt) into 1 - cos^2(wt) x = Acos(wt) so x^2/A^2 = cos^2(wt) Plug in cos^2 |
| Practical for SHM spring constant | F = kx N2L F = ma kx = -ma SHM a = -w^2 x plug in k x = mx w^2 k = m w^2 w = 2pi/T plug in Simplify |
| Angular frequency and angular velocity | Same thing. Both rads^-1 |
| Isochronous oscillations in SHM | Amplitude independent of time period |
| acoswt vs asinwt | Depends on where it starts. (cos is starting from max, sin from equilibrium) |
| Pictures 13/11/25 pag method for g | |
| e.g. Mean water height 3.5m amplitude 1.6m | Find x using amplitude 1.6m, then add to 3.5m. |
| For the plus minus | KEEP SIGNS WHEN NEEDED. Use +- when relevant |
| Total energy of SHM for energy against displacement | Constant = kinetic + elastic potential When energy on y against displacement, KE is a sad curve, PE is a happy curve. Sum to the total at all values of displacement |
| Energy of SHM for energy against time | cos^2 graph for KE and phase shifted by pi for PE. ALWAYS ABOVE ZERO Easiest to do a few points to show pattern, often |
| Pictures 20/11/25 for all 5 graphs to memorise | |
| Free vs forced oscillations | Free vibrates at natural frequency when energy is added initially. Forced is forced by a force to vibrate at a particular frequency of the thing vibrating it - the driving frequency |
| Resonant frequency of pendulum | 1/(2 pi) x root(g/L) Given in questions. Bartons's pendulum - the length of string (with light mass) with the correct length will have a resonant frequency of the driver frequency (the heavy mass) |
| Natural frequency | All systems have a natural frequency - frequency at which they will vibrate if given energy initially |
| Resonance | For a forced oscillator with negligible damping, resonance occurs when driving frequency = natural frequency of oscillator We only focus on first harmonic rlly Causes oscillator to absorb energy VERY efficiently, so amplitude very big |
| Uses of resonance | MRI, microwaves, radio tuning |
| Microwaves | Molecules well represented as spring mass systems. Microwaves at resonant frequency of the springs will transfer a lot of energy to the water. KE so temp. |
| (better to skip) Amplification of instrument noise | Amplification is of the sound box from the sound already made by the instruments, not the strings themselves. |
| Damping | Methods of taking energy out of system. |
| Damping of power cables | Springs with heavy masses hung from cables. When wind, pressure changes above and below wire, so oscillation, so the heavy masses absorb a lot of the energy from the cables, so the cables don't resonate. (masses shouldnt then resonate cables) |
| Damping of car suspension | Springs so no heavy bumps, but would then oscillate uncomfortably. Shock absorber is a piston then submerged into thick oil so takes a while for the spring to move back to start. |
| Types of damping and how they look on displacement vs time graph | Lightly damped - amplitude gradually reduces but still rising and falling. Heavily damped - gradually curves down in slight ramp shape to the x axis. Critical damping - faster ramp curve to equilibrium without overshooting like lightly |
| e.g. of lightly damped | Pendulum in air |
| e.g. of heavily damped | Pendulum in treacle |
| Amplitude vs frequency graph for damping (dont mess up with the displacement time one) | Very sharp normal distribution shape peaking at resonant frequency. No damping is technically infinitely tall. Line is lower the more damping happening - most difference between the lines at the peak. |
| Small point about the peak of the amplitude frequency graph with damping | Adding damping reduces resonant frequency marginally. Peak should be slightly to the left. |
| sinusoidal | Only applies without damping (exponential superimposed) |
| Shock absorbers | Movement in that direction has energy taken out of it so shock absorbers warm slightly. For hanging ball in skyscraper, the absorbers take energy out no matter which way the building moves to the ball |
| Ground resonance | Helicopter blades trap column of air which resonates, then standing wave, which then oscillates body of helicopter, tearing it apart unless you take off. |
| Natural frequency of damper system | Its oscillations will be closer to nat frequency of tower so the sphere can drive well - allows max damping of tower/amplitude of sphere |
| 'small angle of oscillations' | Less than 10 degrees |
| Points for SHM experiment | Fiducial marker, protractor to ensure less than 10 degrees, measure length of string to centre of bob. |
| Amplitude of a wave that varies from 318 to 298 | Amplitude is 10 |
| Vertical spring concepts | Normally we only consider EPE for PE of spring. But must consider GPE for vertical. EPE no longer 0 at equilibrium (now equal to 0.5ke^2 at equi with a new max/min). |
| How does the graph show SHM | Shows a proportional to -x *because negative gradient through origin* - TALK ABOUT THE GRAPH SHAPE |
| Spring relationship between E, F, and x | Look at the springs section of formula booklet. There's a 1/2 in there unlike the normal work done equation. |
| Damping force | Always opposite in direction to v and maximum when displacement is zero. a not involved at all. Depends on v so max force when v is max for max energy dissipation. Say the t = for when v is maximum. Happens when air resistance/friction greatest |
| Check photos 4/12/25 |
Created by:
Pyrogearos2