<p> Export Specific User Parameters ... i.e plotting function </p>

b6627b4e-bd9a-4b65-a19d-f76b58e7473f 9 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

https://mathcurve.com/courbes2d/pendule/pendule.shtml

k 1 - ≥

b 1.25 : a 1 : k 0.75 - : 13 mat

0.75 k x a / cos + sqrt * ± 1 k x a / cos + sqrt * ± 1.25 k x a / cos + sqrt * ± 3 1 sys

x b y b k x a / cos + sqrt * ± :

x 0.75 y x 1 y x 1.125 y x 1.25 y 4 1 sys

https://math24.net/nonlinear-pendulum.html

Pendulum Homogeneous DE ...

2nd Order Type 3

UnitStep 1 ≡ UnitLinear t ≡ UnitGrow d t * exp ω * ≡ UnitDecay d t * - exp ω * ≡ Fails Dirac Integral t sqrt ≡ 51 line

t sqrt t s laplace maple π sqrt 2 s 2 nthroot 3^* /

final rest position datum 0 :

t ω d q datum :

s ω d L t ω d q t s laplace maple :

This Smath document reproduces 1/1 the original Mathcad 11. Seeminly, unique ... NO other CAS

s ω d L 0

s F Y0 s - m - (* Y1 - s ω d L - s 2^s m * + n + (/ (- :

Laplace solver homogeneous ODE c/w forcing function, parameters and initial conditions.

solution is wild wrt parameters and assigned to a function wrt parameters. Y0 Y1 m n ω t fnct s F t 0 > assume s t invlaplace maple 11 line :

Export the solution wrt the DE parameters  ... a long expansion that will solve for any [Y0,Y1, m,n] Y0 Y1 m n ω t fnct m t * 2 / - exp Y0 m 4 n * m 2^- sqrt 4 n * m 2^- sqrt t * 2 / sin * 4 n * m 2^- sqrt t * 2 / cos m * - (* 44 n * m 2^- sqrt t * 2 / cos * n * + (* 24 n * m 2^- sqrt * Y1 * 4 n * m 2^- sqrt t * 2 / sin * + (* 4 n * - m 2^+ / -

Y0 1 :

Y1 0 :

m 0.5 :

n 1.5 :

<p> Export Specific User Parameters ... i.e plotting function </p>

The RHS algorithm is the solution
wrt user parameters, assigned f(t).
OBSERVE: ►  ω is wild ... from L(s,ω,d) t f Y0 Y1 m n ω t fnct :

Export this elegant user solution ... 
Optimiz: NONE ... copy/paste the RHS t f t 4 / - exp 2312 /^* 2312 /^t * 4 / sin * 23 / t 4 / - exp 2312 /^t * 4 / cos * +

d 0.5 :

ω 1 :

Observe: in the conditional the text "" blanks the trace ... same as Mathcad .

x f x 0 ≥ ( x 20 ≤ ( & cases

1. exp(-d*x)*ω generalised decay 2. exp(d*x)*ω generalised grow 3. ω=1 ... UnitGrow/UnitDecay 4. 'd' sets the shape

d x * exp ω * d x * - exp ω * 2 1 sys

100 f 0