Author Topic: Simple Harmonic Motion (SHM)  (Read 6211 times)

Fu-Kwun Hwang

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Simple Harmonic Motion (SHM)
« on: January 30, 2012, 10:20:58 am »
This is a simulation for simple harmonic motion:
$F=m frac{dv}{dt}=-k*x$;

For the purpose numerical calculation, the above second order differential equation is transformer into two equations (first order differential equation):
$frac{dx}{dt}=v_x$ // use this equation to calculate $x(t+dt)$ from $x(t)$ and $v_x(t)$
$frac{dv_x}{dt}=-k*x/m$ // use this equation to calculate $v_x(t+dt)$ from $v_x(t)$ and $x(t), k, m$

With two initial conditions: $x(0)$ and $v_x(0)$, the rest of $x(t)$ and $v_x(t)$ can be calculated.
  

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