I don't agree with some of your equations. Attached is Prime 4 express. It has some problems too--Idon't like the angle plot, but my length plot is better than yours!
Obviously I was'n looking at your sheet with the necessary care.
But I guess Valery should know what exactly to change.
You have no ode for L, no derivative. So you can't demand an initial condition for L The initial value L(0s) is dependent on alpha(0s) and alpha'(0s).
I have rewritten the block, nut still no success (at least we have a different error message now 😉
You may want to recheck your equations.
Thanks, Fred and Werner! See picture and attach!
One problem - Mathcad 15 sheet does not work. But after the converting into Prime - all OK! Why?
Solution without animation is not solution!
When alpha_0 < 7 deg - we have a balance of three energies
When alpha_0 > 7 deg - we have no balance of three energies
I know that alpha=sin(alpha) at alpha <7 deg!
See please The Prime 6 sheet in attach!
There are three energies listed, but two of them are potential energy--the energy stored at the ends of the swing, and the energy stored in the compressed or stretched spring. These must be out of phase with the kinetic energy of the swinging pendulum; that's the nature of a harmonic oscillator (which this is.)
But that's not what your sheet shows
I can get to here
But something still isn't right.