0943b4ce-7088-401b-ae06-eed7d9e032e4 17 6 9 decimal

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Mass spring damped system

Damped system in continuous time ... η => damping coefficient.
f(2), g(2) go in pair with "init" 2 f 2 g init NumIt dt dynSys t init : u t : k 1 NumIt range t t dt t t r g f * + eval : u u t augment : 21 line for u 41 line :

Linear system with 2 states and 1 input: unit step response 'K=1'.

M 1 : η 0.75 : K 0.5 : 31 line

initial condition init 0021 mat :

n 150 : number of samples ≡ step 0.1 : increment size ≡ K step input ≡ 31 line

For "zoom detail" of the front end <= decrease step size. <= experiment various 'K'

The mass-spring differential system X u MasSprDmp 1 M / u 1 el η X 1 el * - 1 K / X 2 el * - (* X 1 el 21 mat :

t r Ctrl 111 mat :

Constant input, i.e. no state feedback in this case

Observe: Ctrl(x,r):=(1)... (1) is neither ... simply 1 ... or (1) 1 in bracket (1) is a unit vector from matrix panel

Sol any1 any2 MasSprDmp any1 any2 Ctrl init n step dynSys :

v Sol 1 row transpose :

s Sol 2 row transpose :

Response sol v1 v2 MasSprDmp v1 v2 Ctrl init n step dynSys : U i 1 n 1 + range idx i el i : for idx sol transpose augment 21 line : U 1 col U 2 col augment U 1 col U 3 col augment 21 mat 31 line :

Auto-index from the canvas var 'x'

v x el s x el K 3 1 sys

Export discrete response

Response 1 el Response 2 el K 3 1 sys