Crankshaft-Driven Pendulum

423844ea-3059-4df9-86e7-b57dd9ffc8dc 52 Crankshaft-Driven Pendulum Fridel Selitsky 4 5 decimal

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slider-crank drive

Crank length OA 0.25 :

crank-rod length AB 1 :

pendulum

length L L 1 :

damping coefficirnt μ μ 0.11 :

mass of bob m m 1 :

bob start speed ω0 ω0 4 :

m/s^2 g 9.81 :

Начальные значения:

φ0 12 / π * :

Δθ π 36 / :

t xA OA Δθ t * cos * eval :

t yA OA Δθ t * sin * :

t ψ t yA AB / asin :

t yB t yA AB t ψ cos * - :

xB 0 :

Подпрограмма расчёта  методом Рунге-Кутта y0 Δt RunKut tM t0 12 / Δt * + eval : K1 Δt t0 y0 f * eval : yM y0 12 / K1 * + eval : K2 Δt tM yM f * eval : yM y0 12 / K2 * + eval : K3 Δt tM yM f * eval : y0 y0 K3 + eval : K4 Δt t0 y0 f * eval : y y0 16 / K1 2 K2 * + 2 K3 * + K4 + (* + eval : 91 line :

Правая часть системы уравнений t y f y 2 el μ m / y 2 el * - y 1 el sin g t yB (t diff (t diff + (* L / - 21 mat :

y 1 el φ ≡

y 2 el ω ≡

Начальные условия t0 0 : y0 φ0 ω0 21 mat : 21 sys

step 0108 range :

D y0 0.06 RunKut : φ D 1 el eval : координаты груза x L φ sin * eval : y t yB L φ cos * - eval : 0 0 t xA t yA xB t yB 3 2 mat xB t yB x y 2 2 mat t 0 ≡ path x y 1 2 mat : path path x y 1 2 mat stack : if 0 0 . 13 blue t xA t yA . 13 blue xB t yB . 20 green 3 5 mat x y . 10 40 m sqrt * + Red 1 5 mat 0 0.6 - 0 1.3 - 2 2 mat 6 1 sys 6 1 line

The pivot of the pendulum is driven up and down by a slider-crank mechanism. This transmits a vertical acceleration to the bob, in addition to the acceleration due to gravity. This results in the equation of motion

where y is the vertical position of the pivot along the slider. The animation traces the movement of the pendulum bob.