In Matlab:

Adapt pend. m to build a damped pendulum with oscillating pivot. The goal is to investigate the phenomenon of parametric resonance, by which the inverted pendulum becomes stable! The equation is y+dy+(lg+Acos2t)siny=0 where A is the forcing strength. Set d=0.1 and the length of the pendulum to be 2.5 meters. In the absence of forcing A=0, the downward pendulum y=0 is a stable equilibrium, and the inverted pendulum y= is an unstable equilibrium. Find as accurately as possible the range of parameter A for which the inverted pendulum becomes stable. (Of course, A=0 is too small; it turns out that A=30 is too large.) Use the initial condition y=3.1 for your test, and call the inverted position "stable" if the pendulum does not pass through the downward position