Energy of simple harmonic oscillator review
|Equation||Symbol breakdown||Meaning in words|
|is the elastic potential energy, is spring constant, and is length of extension or compression relative to the un-stretched length.||The elastic potential energy is directly proportional to the square of the change in length and the spring constant.|
|is change in gravitational potential energy, is mass, is the gravitational field strength, and is change in height.||The change in gravitational potential energy is directly proportional to mass, gravitational field strength, and change in height.|
|is translational kinetic energy, is mass, and is the speed.||Translational kinetic energy is directly proportional to mass and the square of the speed.|
How to find energy over time for a simple harmonic oscillator
Elastic potential energy
- occurs when the system is at the maximum displacement of and .
- occurs when the system is at .
- occurs when the system is at its maximum speeds and .
- occurs when .
- occurs when . This happens at the endpoints of the oscillation where the system momentarily stops () at the maximum displacement.
- occurs at . This is when the system is moving through the equilibrium position () and has its maximum speed.
- is constant, so .