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Help please with ODE solution

ValeryOchkov
Ruby I

Help please with ODE solution

 

Pendulum-Hook.png

12 REPLIES 12

Re: Help please with ODE solution

Did you forget to attach the Prime sheet with the error?

Re: Help please with ODE solution

Sorry!

See lease the attach

Re: Help please with ODE solution

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!

Re: Help please with ODE solution

Here is what we get using Freds modified equation for L(t)

Werner_E_0-1607966150718.png

 

Re: Help please with ODE solution

Note that I also questioned the sin(alpha) term in the first equation.  Force due to gravity is vertical . . .

Re: Help please with ODE solution

Obviously I was'n looking at your sheet with the necessary care.

But I guess Valery should know what exactly to change.

Re: Help please with ODE solution

Yer - see please in attach the energies analyzse. 

Re: Help please with ODE solution

Attached fixed previous error

Re: Help please with ODE solution

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.

Werner_E_0-1607965445392.png

 

Re: Help please with ODE solution

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!

pendulum-polar.png

Tags (1)

Re: Help please with ODE 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!

Re: Help please with ODE solution

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

Fred_Kohlhepp_0-1608135242297.png

I can get to here

Fred_Kohlhepp_1-1608135341801.png

But something still isn't right.

 

 

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