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Definition
| One full cycle of motion is from maximum height at one side to maximum height on the other side then back to the first side. |
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LOWEST POINT OF AN OSCILLATION |
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Definition
| Is the equilibrium point; in motion the object is said to oscillate about equilibrium |
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DISPLACEMENT OF THE OBJECT |
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Definition
| From equilibrium changes during motion: decreases as returns to equilibrium; reverses and increases moving away from equilibrium in opposite direction; decreases as it returns to equilibrium; increases as it moves away from equilibrium towards starting position |
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Definition
| Maximum displacement of the oscillating object from equilibrium |
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Definition
| Constant amplitude with no frictional forces |
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Definition
| Time for one complete cycle of oscillations |
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Definition
| Number of cycles per second |
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Definition
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Definition
If two things do not oscillate correspondingly they have a phase difference because they are not in phase.
Phase difference in radians = 2∏♦t / T |
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PHASE DIFFERENCE IN DEGREES |
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Definition
2∏ radians = 360º
so phase difference = 360 x ♦t / T |
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PRINCIPLES OF SIMPLE HARMONIC MOTION |
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Definition
| Oscillating objects speed up as it returns to equilibrium; slows down when it moves away from equilibrium |
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VARIATION OF VELOCITY WITH TIME |
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Definition
| Gradient of the displacement time graph |
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WHEN IS VELOCITY GREATEST? |
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Definition
| When gradient of displacement time graph is greatest; at zero displacement |
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VARIATION OF ACCELERATION WITH TIME |
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Definition
| Gradient of velocity time graph |
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WHEN IS ACCELERATION GREATEST? |
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Definition
| When gradient of velocity time graph is greatest so when velocity is zero and displacement is maximum in opposite direction |
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WHEN IS ACCELERATION ZERO? |
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Definition
| When displacement is zero. When gradient of velocity time graph is zero |
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ACCELERTATION AND DISPLACEMENT |
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Definition
| Acceleration is always in the opposite direction to the displacement (opposite signs) |
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Term
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Definition
The oscillating motion in which the acceleration is proportional to the displacement and always in the opposite direction to the displacement
acceleration = -constant x displacement
a = -(2∏f)2x |
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WITH SINE AND CO SINE CURVES |
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Definition
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Term
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Definition
| Resulting force acting toward the equilibrium position ALWAYS |
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Term
RESTORING FORCE, ACCELERATION AND DISPLACEMENT |
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Definition
| If the restoring force is proportional to the displacement to equilibrium, acceleration will also be equal to displacement (always towards equilibrium) THE OBJECT OSCIALLATES WITH SIMPLE HARMONIC MOTION |
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Term
TWO STRETCHED SPRINGS AND A TROLLEY |
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Definition
Half cycel can be recorded using a ticker tape attatched to one end of the trolley. When trolley is released, the ticker timer prints dots on the tape at 50 dots per second.
Graph of displacement against time can be plotted which can measure time period
Motion sensor linked to computer can record osciallting motion |
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Term
CHANGING THE FREQUENCY OF THE OSCILLATIONS OF A LOADED SPRING |
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Definition
Adding extra mass - increases interia; at certain displacement trolley would be slower without extra mass. INCREASING TIME FOR EACH CYCLE
Weaker springs - Restoring force would be less at any given displacement , so INCREASES TIME FOR EACH CYCLE OF OSCILLATION |
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Term
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Definition
An object oscillates with a constant amplitude because there is no friction force acting on it.
Only forces acting on it combine to form the restoring force.
If friction was present, the amplitude of oscillations would gradually decrease and stop
Friciton is usually present even if you can't see the change in amplitude after one cycle |
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Term
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Definition
At maximum displacement, velocity is 0 so potential energy is at it's maximum and kinetic energy is 0
At 0 displacement, velocity is at it's maximum so potential energy is 0 and kinetic energy is maximum |
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Definition
| Total energy of system remains constant and equal to maximum potential energy |
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Definition
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Term
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Definition
| When dissipative forces are present |
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Term
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Definition
| Dissipate the energy of the system to the surroundings as thermal energy. |
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Definition
Time period is independent of amplitude.
Each cycle takes the same length of time as the oscillations die
Amplitude gradually decreases reducing by the same fraction each cycle. |
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Term
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Definition
Just enough to stop the system oscillating after it has been displaced and released from equilibrium.
Oscillating object returns to equilibrium in shortest possible time without over shooting. Important in mass spring systems such as vehicle suspension. |
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Definition
| Damping is so strong that the displaced object returns to equilibrium much more slowly than if it critically damped. No oscillating motion occurs. e.g mass on a spring in thick oil. |
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Definition
| A coiled spring near each wheel, between wheel axle and car chassis. When wheel is jolted , the srping smoothes out the force on the jolts. The oil damper fitted with each spring prevents the chassis from bouncing up and down too much. Flow of oil through valves in the piston of each damper provides frictional force that damps oscillating motion. Dampers ensure chassis returns to equilibrium in the shortest possible time - so close to critical damping |
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Definition
| E.g pushing someone on a swing |
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Definition
Pushes on a swing are an example.
Force that varies regularly in magnitude with a definate time period |
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Term
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Definition
| When a system oscillates without a periodic force being applied to it |
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Term
AS APPLIED FREQUENCY REACHES NATURAL FRQUENCY OF THE MASS - SPRING SYSTEM |
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Definition
The amplitude of oscillations of the objects increase more and more
Phase difference between the displacement and periodic force increases from zero to 1/2∏ at the natural frequency |
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Term
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Definition
Applied frequency is equal to natural frequency of mass spring system
Amplitude of oscillations become very large; lighter the damping, the larger the amplitude becomes
Phase difference between displacement and the periodic force is 1/2∏
Periodic force is in phase with the velocity of the oscillating object. |
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Term
APPLIED FRQUENCY GREATER THAN NATURAL FREQUENCY |
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Definition
Amplitude of oscillations decrease more and more
Phase difference between displacement and periodic force increases from 1/2∏ until it is ∏ out of phase with the periodic force. |
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Term
WHEN IS THE AMPLITUDE GREATEST |
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Definition
When applied frequency is equal to natural frequency providing damping is light
here:
applied frequency of periodic force =
natural frequency of a system |
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Term
OSCILLATING SYSTEM WITH LITTLE OR NO DAMPING AT RESONANCE |
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Definition
| Applied frequency of periodic force = natural frequency of system |
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Term
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Definition
The periodic force acts on the object at the same point in each cycle causing the amplitude to increase to a maximum value limited only by damping.
Max amplitude, energy supplied by periodic force is lost at the same rate because of the effects of damping |
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Term
APPLIED FREQUENCY AT RESONANCE |
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Definition
Resonant frequency = natural frequency when there is little/no damping
The lighter the damping, the closer the resonant frequency to natural
Resonance occurs at a slightly lower frequency than natural |
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Term
PENDULUMS OF THE SAME LENGTH |
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Definition
| If one pendulum is displaced, the other of the same length is forced to oscillate too and responds much more than if it were at any other length. It has the same time period so same natural frequency so oscillate in resonance. Response of other lengths depends on how close they are to initial pendulum. |
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Definition
If wind speed means the periodic force is equal to natural frequency, resonance can occur in absence of damping
e.g collapse bridge |
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Term
STEADY TRAIL OF PEOPLE ON A BRIDGE
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Definition
| With insufficient damping, people in step with each other can cause resonant oscillations |
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