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25 Cards in this Set
- Front
- Back
SHM definition |
An oscillation in which the acceleration of an object is directly proportional to its displacement from the midpoint (equilibrium position), and is directed towards the midpoint |
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Amplitude |
maximum displacement from the midpoint |
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Kinetic + Potential Energy |
Mechanical Energy - stays constant if undamped |
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Cycle of Oscillation |
maximum positive displacement to maximum negative displacement and back again |
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Force on spring |
F = -kx
k: spring constant |
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Period of mass oscillating on a spring |
T = 2π √(m / k)
k: spring constant |
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Investigating the Mass-Spring System (Setup) |
- Trolley attached between 2 springs, one joined to a fixed point and the other to a force meter and data logger
- I/\/\/\/\/\/-(Trolley)-/\/\/\/\/\/\I----(Data logger)
- Data logger draws displacement-time graph to show T |
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Investigating the Mass-Spring System (Method) |
- Pull to one side by certain amount & let go - Change mass by loading trolley with masses (include mass of trolley in calculations) - Change k with different spring combinations - Change A by pulling across different amounts |
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Investigating the Mass-Spring System (Results) |
- T ∝ √m -so- T^2 ∝ m
- T ∝ √(1/k) -so- T^2 ∝ 1/k
- T doesn't depend on A |
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Period of pendulum |
T = 2π √(l / g)
l: distance between pivot & centre of mass of the bob |
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Free Vibrations |
- Oscillates at natural frequency and no energy transferred to the surroundings
- Never happens, but in air vibrations caused free |
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Driving Frequency |
Frequency of periodic external force causing a system to vibrate |
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Resonance |
Driving frequency = natural frequency
As driving frequency approaches natural frequency system gains more and more energy vibrates with rapidly increasing amplitude |
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Resonance examples |
Organ Pipe - Column of air resonates, driven by motion of air at the base Swing - Resonates when someone pushes it at its natural frequency Glass Smashing - When driven by sound wave at right frequency Radio - Tuned so electric current resonates at same frequency as the desired radio station |
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Damping Forces |
Force that causes oscillating system to lose energy (usually frictional / air resistance)
Systems often deliberately damped to reduce resonance
Car shock absorbers damp by squashing oil through a small hole when compressed |
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Damping & Amplitude / Frequency |
Damping reduces the amplitude of the oscillation over time and reduces the frequency by a set amount |
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Critical Damping |
Stops oscillations in the shortest possible time as the two forces balance eachother
Car suspension & loud speakers are critically damped so they don't oscillate |
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Overdamping |
Heavier damping than critical damping. Damping overwrites spring and prevents it from reaching rest position. It approaches equilibrium. No oscillation
Door damping / non-slam |
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Underdamping |
Amplitude decreases over time but does not reach zero (musical instruments) |
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Lightly Damped Resonance Peak |
Very sharp. Amplitude only increases dramatically when driving frequency very close to natural frequency |
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Heavily Damped Resonance Peak |
Flatter. Amplitude doesn't increase so much close to natural frequency and is less sensitive to the driving frequency |
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Natural Frequency
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The frequency at which a system will vibrate freely
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Periodic motion
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The regular, repetitive motion of a body which continually retraces its path at regular intervals
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Damping
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The process whereby energy is taken from the oscillating system
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