Important Definitions
- Periodic Motion- Motion repeated in equal intervals of time
- Restoring force- Force that pushes/pulls the object back towards equilibrium so in the opposite direction of the displacement (force restores the object back to equilibrium)
- Simple harmonic motion- Restoring force is proportional to the displacement of the object or the object has a sine/cosine position-time relationship. The maximum displacement is therefore equal on both sides
- Equilibrium position- Position in which a vibrating object resides when not disturbed
- Amplitude (A)- Maximum displacement of the vibrating object from its equilibrium position
- Period (T)- Time interval needed for the object to make one complete cycle (seconds)
- Frequency (f)- How many cycles in one second
- f = 1/T and the units are s^-1 or Hz
- Angular frequency- ω (number of rotations in one second)
This Youtube video provides an overview of simple harmonic motion and starts to explain some of the next parts of the content page. It is a great way to introduce simple harmonic motion or to have a general understanding. |
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Energy Transfers
Energy continuously transfers between kinetic and potential energy as an object moves in simple harmonic motion. When the object is at its maximum displacement, the energy is all potential energy (not moving and the spring is stretching the most). On the other hand, the object has all kinetic energy as it passes through its equilibrium position because it has the greatest velocity then and no potential energy because the spring doesn't stretch at all.
Variables that Affect Period
Period (T) = 1/Frequency = 2π / ω
Period of a Spring is affected by
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Period of a Pendulum is affected by
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Inertial vs. Gravitational Mass
Inertial Mass- An object's mass based on its ability to resist change
Gravitational Mass- An object's mass based on the gravitational field strength
These masses are equal (mass is constant)
Finding inertial mass: Put an object into simple harmonic motion using a spring with a known spring constant and find the period, and then use that to solve for mass
Gravitational Mass- An object's mass based on the gravitational field strength
These masses are equal (mass is constant)
Finding inertial mass: Put an object into simple harmonic motion using a spring with a known spring constant and find the period, and then use that to solve for mass
Determining whether or not motion is SHM
Reviewing the definition: Simple harmonic motion means that the restoring force is proportional to the displacement and the object has a sine/cosine position vs. time relationship
- Look for the sine/cosine type of graph and if this isn't there, then it is not simple harmonic motion
Determining Wavelength or frequency from a picture
The period is the amount of time it takes to complete one cycle, so looking at a graph you have to find the change in time between two points coming from the same direction. The distance between peaks is the easiest, as shown in the picture. The frequency is 1 / Period, so once you find the period from the graph it is easy to find the frequency.
You can find the amplitude by measuring the distance from the equilibrium position (where the graph changes concavity) to the maximum or minimum point because this will be the maximum displacement. The wavelength formula is shown below, and it is the distance traveled in one period. In order to find it, you need to know the velocity of the wave, and you can calculate the frequency by finding the period and then using f = 1 / T |
Connecting different representations
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