I am trying to solve and plot the differential equations for springs. when the damping factors are under 1 (underdamping), I tried damping ratios of: 0.01, 0.2, 0.1, 0.4, 0.8 If I use the following equations (wd= damped frequency, wn= natural frequency, v0= v initial, x0= x initial, t= time) wd=wn*sqrt(1-z^2); A=sqrt(((v0+z*wn*x0)^2+(x0*wd)^2)/(wd^2)); phi=atan((x0*wd)/(v0+z*wn*x0)); x=A*exp(-z*wn*t)*sin(wd*t+phi); and when I use the initial conditions wn=2, x0=1, v0=1 I get the following picture http://imageshack.us/photo/my-images/191/24265826.jpg/ Why does the value of x not decrease and increase instead at the start? (Shouldn't the value of x not exceed initial value?) Is there something wrong with the equation I have formed above? Or is this what usually happens when solving these spring systems?