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Title: A pendulum connected to a springPost by: concord on August 21, 2005, 08:09:59 pm
A pendulum connected to a spring:
http://mw.concord.org/modeler1.3/mirror/mechanics/pendulum3.html (http://mw.concord.org/modeler1.3/mirror/mechanics/pendulum3.gif) Title: Re: A pendulum connected to a springPost by: Fu-Kwun Hwang on February 17, 2010, 04:35:53 pm
The following is an EJS version of the above applet (with more options)
You can drag the spring, particle and the rod with mouse click/drag. You can change spring constant k, mass m , spring length L, and damping constant b. Enjoy it! Title: Re: A pendulum connected to a springPost by: Fu-Kwun Hwang on October 24, 2011, 12:51:49 pm
Equation used in the above simulation.
Assume angle $\theta$ for the pendulum, angular velocity $\omega=\frac{d\theta}{dt}$ And $\frac{d\omega}{dt}=calAplha(\theta)+ g\cos\theta+ -b\omega/m$ where $caAplha(\theta)$ calculate spring force and find it tangential component. Code: public double calAlpha (double c) { cs=Math.cos(c); sc=Math.sin(c); x=x2-R*cs; y=y2-R*sc; L=Math.sqrt((x-x1)*(x-x1)+(y-y1)*(y-y1)); f=-k*(L-L0); fx=f*(x-x1); fy=f*(y-y1); n=-fx*cs-fy*sc; nx=-n*cs; ny=-n*sc; fx=fx-nx; fy=fy-ny; if(c>0)sign=-1; else sign=1; return sign*Math.sqrt(fx*fx+fy*fy)/I; // where I is the momentum of initial } |