The DeCantgo doll Gif makes up for the inexcusable doubling up of the shaky bridge gif earlier, Marcia.
It's the Tacoma Narrows Bridge. Didn't you take calculus in High School? It's easily explained here...
Mathematically, the force generated from such cable-like springs have the form
if d>0, then Fs = - k d, and if d<0, then Fs=0.
where k is the spring constant and d is the displacement from equilibrium of the spring.
The kinetic energy consists of two parts, the kinetic energy of vertical motion
(m/2) (dy/dt)2
and the kinetic energy of the torsional motion, which turns out to be
(m/6) L2 (dx/dt)2
where L is the beam length.
Similarly the potential energy has two parts, -mgy the potential energy of the vertical displacement, and the potential energy due to torsional rotation angle x,
(K/2) [ ( y - (L/2) sin x )+ + ( y + (L/2) sin x )+ ]2
where the ( )+ means it contributes only if the term is positive, i.e. it accounts for the cable-like springs.
The equation of motion is derived by minimizing the total energy L = T - V, i.e. we differentiate the energy with respect to time and set the result equal to zero. Then a small viscous dissipation term is added and if the springs never lose tension, the resulting equation for the torsional motion is <
x'' + c x' + k sin(x) cos(x) = f(t)
and for the vertical motion is
y'' + c y' + (k/3) y = g.
Got it?