Overview of equations and skills for the energy of simple harmonic oscillators, including how to find the elastic potential energy and kinetic energy over time. Understand how total energy, kinetic energy, and potential energy are all related.
|Meaning in words
|The elastic potential energy is directly proportional to the square of the change in length and the spring constant.
|The change in gravitational potential energy is directly proportional to mass, gravitational field strength, and change in height.
|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
Elastic potential energy depends upon the position of our system, so a position vs. time graph can be used to find the elastic potential energy
over time for a simple harmonic oscillator. There are a few important points to note when comparing the position and energy graphs: occurs when the system is at the maximum displacement of and . occurs when the system is at .
depends upon the speed of a system, so a velocity vs. time graph can be used to find the kinetic energy over time for simple harmonic oscillator. There are a few important points to notice when comparing the velocity and energy graphs: occurs when the system is at its maximum speeds and . occurs when .
The total energy is the sum of the kinetic and elastic potential energy of a simple harmonic oscillator:
The total energy of the oscillator is constant in the absence of friction. When one type of energy decreases, the other increases to maintain the same total energy.
There are a few important points to keep in mind about energy:
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 .
To check your understanding and work toward mastering these concepts, check out our exercises:
Want to join the conversation?
- how do you calculate Kmax and Us, max(3 votes)
Us, max is 1/2kA^2, where A is the Amplitude and k is the spring constant.
Kmax is 1/2m(v,max)^2 where m is mass(8 votes)