Consider a uniform $10$m long beam, with flexural rigidity of $120,000$N m$2,$ and a linear density of $\backslash$rho $=80.$

The beam has fixed supports at both ends, and a weight is hung under the beam$$attached via cable at the

x $=3$ point$$applying a downward force of $100$ N $.$ At the same time a winch is connected to the beam$$via

a cable attached at the x $=7$ point$$pulling upward with a force of $100$ N $.$

The deflection function of the beam, in mm$,$ is given by

y$($x$)=1$

$900$

$($

$125(($x $3)3$H$($x $3)($x $7)3$H$($x $7))71$x$3+315$x$2)$

Note: you do not need to derive this yourself for this assignment, although you are encouraged to verify it$.$

However, the cables used weren$$t rated for this force, and they both snapped at precisely the same time.

One moment there was a load causing the beam to deflect, and the next moment there wasn$$t$.$

With the sudden removal of the load, the beam vibrated.

We do not know why the beam was configured this way, nor why weak cables were used. We think a bet

and maybe alcohol was involved, but nobody will admit to any knowledge about the beam $($or how it came

to be configured this way$)$ at all.

Solve the beam vibration problem for this beam after the load disappeared. You should consider that the

instant the cables broke was at time t $=0.$

You can presume that the initial partial derivative with respect to time is ut$($x$,0)=0.$

Have Desmos $($or other computer software of your choice$)$ produce an animation of the vibrating beam