derive an equation to represent this mass spring damper in terms of input fore $F$ and relates to output displacement $(x)$
when springs $K_1=3$ , $K_2=5$ damper $C=6$ and mass $M=1$ , $F$ is a step of $10$
[Math] derive an equation for this mass spring damper
ordinary differential equationsphysics
Best Answer
You just need to use Newtons law $\sum F=ma$. You have the forces:
The corresponding forces of a spring and a damper are $F_k=-kx$ and $F_c=-c\dot x$. So you have
$$ m\ddot x=-(k_1+k_2)x-c\dot x+F. $$
Finally you obtain the usual equation
$$ m\ddot x+c\dot x+(k_1+k_2)x=F. $$
Tip: although I assume you are just learning this topic, I suggest you first read any book on elementary mechanics (this ideology can be extended to any field of study). This is a classical example and many books treat this problem. It is also always good to show that you have tried something in advance and not let people just answer for you. It is always good to help, but it is always better to help knowing that you've already given it a try.