Energy of SHM

Last updated 2023.01.13 Edit Source

• Physics
• Dynamics
• Harmonic motion

minimum energy at_ stable equilibrium_
kinetic E + elastic E = energy
$E=E_k+E_e$

at extreme position ($x_{max}=A$)

$E_k=0$
$E_e=\frac{1}{2}k\cdot A^2$

When no kinetic energy
$E=\frac{1}{2}kA^2$

at equilibrium position ($x=0$)

$E_e=0$
$E_k=\frac{1}{2}mv^2$

When no elastic energy
$E=\frac{1}{2}mv^2_{max}$

Energy remains constant
$\frac{1}{2}kA^2=\frac{1}{2}m\omega^2\cdot A^2=\frac{1}{2}mv^2_{max}$

The maximum kinetic energy is equal to the maximum elastic energy

undamped SHM