Recent content by Incud2

Ehm, I just wanted to find (1) r, the solution of the problem, but also (2) the equation of motion. I wasn't able to find the solution. Now both the points seems clear to me. I produced a well written document for anyone who want to read the solution without having to read the whole thread which...

Still not a completely correct solution, here's an update:

@Cutter Ketch I think I've understand the concept. I have written the exercise in Latex, presented in a clearer way. You can see it in the attachments. If you find any error please pm me.

@tnich Thank you very much. The last thing I miss is about the initial conditions. The coefficients are $$m=5,\quad s=\frac{mg}{\Delta x} = 490.5, \quad r=\sqrt{4ms}=99$$ So the differential equation describing the system is $$5\ddot x+99\dot x+490.5x=490.5$$ [not required by the exercise] I...

@Cutter Ketch The only thing I found there - the 300th time I read the chapter - is the formula (which does not consider gravity) of maximum displacement in horizontal damped motion:$$x_{max} =x(t=1/\omega_0)=2mV/(re)$$ where V is the initial velocity. What formula are you referring to? @tnich...

Another idea. If I change the coordinate system in order to have x(t=0) = 10cm and x(t=infinity) = 0 I can have initial conditions $$A=10cm=10^{-1}m; \quad B=\frac{r}{2m}$$ Edit: with these initial conditions, I obtain that the velocity is zero constant. How is it possible I don't see useful...

Thank you both for your replies. I think I can use the energy formula $$ E = \frac 1 2 m \dot{x} ^2 + \frac 1 2 s x^2$$ At time 0 there is no kinetic energy (is the pan in rest position?) so the energy is, according to my coordinate system $$ E(t=0)=0$$ At time infinity there is no kinetic...

Homework Statement This problem is taken from Problem 2.3, Introduction to Vibration and Waves, by H.J. Pain and P. Rankin: A critically mechanical system consisting of a pan hanging from a spring with a damping. What is the value of damping force r if a mass extends the spring by 10cm without...