deriving equation of motion

Nov 2019
22
1
UK
Hi everybody,

I'm stuck on a question deriving an equation of motion for this problem.

"Three particles, B, C and D, of masses 1 2m, m and m, respectively, are connected to three springs as shown in the following diagram. The left-hand spring is connected to a fixed point A, and the particles are constrained to move in a straight line on a smooth horizontal surface. Each spring has natural length 10. Spring AB has stiffness 2k, spring BC has stiffness 3k, and spring CD has stiffness k. The particles are displaced from their equilibrium positions and released. The displacements of the particles B, C and D from their equilibrium positions are x1, x2 and x3, respectively, and time t is measured from the instant when the particles are released."

It wants the answer to be
$\begin{matrix}
\text{(k/m)} & -10 & 6 & 0 \\
& 3 & -4 & 1 \\
& 0 & 1 & -1
\end{matrix}$

(Matrix form)

Appreciate any help,

Thank you.
 

skipjack

Forum Staff
Dec 2006
21,493
2,476
Can you post the diagram?
 

skeeter

Math Team
Jul 2011
3,365
1,856
Texas
You might want to take a look at this post on the physics stack exchange ...