a9e3f6d2-b5fe-4eb8-99bf-ce501e4b80e3 5 Martin Kraska 3 5 false false 0 7 decimal

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

L 1 m * :

m 20 g * :

g g.e :

n 40 :

φ.0 100 ° * :

φ.1 100 ° * :

t.1 2 s * :

m L * t φ'' * m g * t φ sin * + 0 ≡

0 φ φ.0 ≡

0 φ' ω.0 ≡

System of equations

S m L t φ'' * g t φ sin * + (* 0 ≡ 0 φ φ.0 ≡ 0 φ' ω.0 ≡ 31 sys

ω.0 S S :

Parametrize

ω.0 φ.e ω.0 S t φ t.1 n rkfixed n 1 + 2 el eval 11 line :

Parametric solution

n.ω 20 :

j 1 n.ω range :

ω j el 3.9 0.2 j n.ω / * + :

P j el ω j el φ.e :

Sampling

x φ.e φ.1 ω P x linterp 3 1 sys x φ.e φ.1 ω P x linterp 3 1 sys

Plotting

x f x φ.e φ.1 - :

Direct solution

x φ.e φ.1 ≡ x 3.8 5 solve #

x f x 3.8 5 solve #

x φ.e φ.1 ≡ x 4 roots #

x f x 4 roots #

x φ.e φ.1 ≡ ω.0 5 ≡ FindRoot #

x f x 5 ≡ FindRoot #

x φ.e φ.1 ≡ ω.0 5 ≡ Broyden #

x f x 5 ≡ Broyden #

4 x φ.e φ.1 ≡ al_nleqsolve #

4 x f al_nleqsolve 4.006 11 mat

4 x g x φ.e φ.1 - 11 line : al_nleqsolve 4.006 11 mat

Solution of the sampled and interpolated function

ω P x linterp φ.1 ≡ x solve 4.006

ω P x linterp φ.1 ≡ ω.0 5 ≡ FindRoot 4.006

M ω.0 S t φ t.1 n rkfixed :

ω P x linterp φ.1 ≡ x 4 roots #

M 1 n 1 + ( range 1 2 1 2 mat el M 1 n 1 + ( range 1 3 1 2 mat el 2 1 sys

lastError diff(#;#) - function is not defined.

M 2 col max ° 172.683