Jairo Sinova Texas A&M University Real time animation of harmonic motion of a spring restart:with(plots): T:=1.0; omega1:=2*Pi/T; A:=1.0; phi:=0.*Pi; f:= t ->A*cos(omega1*t-phi); plot([t,f(t),t=-1..2*T],view =[-1..2*T,-2*A..2*A]);

JCIjNSEiIg==

LCRJI1BpRyUqcHJvdGVjdGVkRyQiKysrKys/ISIq

JCIjNSEiIg==

JCIiIUYj

Zio2I0kidEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiZJIkFHRiUiIiItSSRjb3NHRiU2IywmKiZJJ29tZWdhMUdGJUYrOSRGK0YrSSRwaGlHRiUhIiJGK0YlRiVGJQ==

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

# this one takes a while to compute pMovie:=NULL: n:=100:NN:=5; Dt:=NN*T/n: tt:=0: for k from 1 to n do tt:=tt+Dt: pframe:=plots[display]([plot([t,f(t),t=0..tt],view =[-1..NN*T,-2*A..2*A]), plot([0.2*cos(t),f(tt)+(A+0.8-f(tt))/(2*Pi*10)*t+0.02*sin(t),t=0..10*2*Pi],view=[-1..NN*T,-2*A..2*A]), plots[pointplot]([0.2,f(tt)],style=point,symbol=circle,color=blue,view=[-1..NN*T,-2*A..2*A])], plot([t,f(tt),t=0.2..tt],view=[-1..NN*T,-2*A..2*A],color=blue)): pMovie:=pMovie,pframe: end do: plots[display](pMovie,insequence=true);

IiIm

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFH