NTNUJAVA Virtual Physics LaboratoryEnjoy the fun of physics with simulations! Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/
July 07, 2020, 04:53:39 am

Wisdom is to bring the best out of our students. ...Wisdom

 Pages: [1]   Go Down
 Author Topic: Simple Harmonic Motion (SHM)  (Read 5959 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
Fu-Kwun Hwang
Hero Member

Offline

Posts: 3085

 « Embed this message on: January 30, 2012, 09:20:58 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.

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)
Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list