A $1$ kg body is attached on a spring. The initial displacement is $x_0=0.5$m then we drop it. The equation which describes movement of mass is:
$\ddot x+3\dot x + 2x=0$.
I have managed to solve the differential equation and got:
Question is: will mass oscillate and what will be it's maximum displacement from equilibrium point?
What I've done:
I calculated motion amplitude ($A^2$=$c_1^2+c_2^2$ $c_1$=-0.5 and $c_2=1$) and my answer is that it will oscillate since it's not critical damping.
I don't think that it's allowed what I've done (I'm not sure if equation for amplitude holds for damped vibration and if amplitude really is maximum displacement). I am also not sure how to find out whether system will oscillate.