Damped harmonic oscillator equation¶
Assuming there is a damping force acting on an oscillating body that is linearly proportional to the body’s velocity, we can write a differential equation for the body’s position. We’re assuming the body only moves in one direction.
Links:
- displacement¶
Displacement of the oscillating body as a function of time. See
euclidean_distance.- Symbol:
x(t)- Latex:
\(x{\left(t \right)}\)
- Dimension:
length
- undamped_angular_frequency¶
Undamped
angular_frequencyof the oscillator.- Symbol:
w- Latex:
\(\omega\)
- Dimension:
angle/time
- damping_ratio¶
damping_ratio, which critically determines the behavior of the system.- Symbol:
zeta- Latex:
\(\zeta\)
- Dimension:
dimensionless
- definition¶
Derivative(x(t), (t, 2)) + 2 * zeta * w * Derivative(x(t), t) + w^2 * x(t) = 0- Latex:
- \[\frac{d^{2}}{d t^{2}} x{\left(t \right)} + 2 \zeta \omega \frac{d}{d t} x{\left(t \right)} + \omega^{2} x{\left(t \right)} = 0\]