Python 2b.py
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Practicum 2
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Trash Panda
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15 apr. 2019 door Trash Panda
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14:53 door mij
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18 feb. 2019
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# -*- coding: utf-8 -*-
"""
Created on Fri Feb 15 11:03:41 2019

@author: olafc
"""
import numpy as np
import matplotlib.pyplot as plt


x0 = 0          #Positie in meters
t0 = 0
t1 = 10
dt = 0.01
v0 = 10         #Snelheid in meters per seconde
P = 10          #Kracht in N
m = 200         #Massa in kilogram
t = np.linspace(t0, t1, int(1+t1/dt)) #Tijd range
def Accelaration(v):
    a = -10*v**3/m
    return a

#integrate 10=>v (v dv)= 0=>s (-10v^3/200 ds)
#integrate 10=>v (dv/v^2)= 0=>s (-10/200 ds)
# 10=>v [-1/v] = 0=>s [-s/20]
# -1/v - -1/10 = -s/20
# -1/v + 1/10 = -s/20
# s/20 + 1/10 = 1/v
# s+2 = 20/v
# v(s+2) = 20
# v = 20/(s+2)
# ds = v dt
# 0=>s ds = 0=>8 20/(s+2) dt
# 0=>s (s+2)ds = 0=>8 20dt
# 0=>s [.5s^2+2s] = 0=>8 [20t]
# 0.5s^2+2s-160 = 0
# volgens abc-formule s=16
# v = 20/18
# v = 10/9
# v at t=8 =10/9
# s at t=8 =16

Pos_num = np.zeros(len(t))
Speed_num = np.zeros(len(t))
Pos_num[0] = 0
Speed_num[0] = v0

for n in range(1, len(t)):
    a = Accelaration(Speed_num[n-1])
    Speed_num[n] = Speed_num[n-1]+a*dt
    Pos_num[n] = Pos_num[n-1] + Speed_num[n-1]*dt

c1 = np.interp(1000, t , Speed_num) #Speed bij t=10
print("v bij t=10:                    ",np.round(c1,3),"m/s")
c2 = Pos_num[800]                   #Positie bij t=8
print("x bij t=8:                     ",np.round(c2,3),"m")
c3 = (16-Pos_num[800])              #error bij t=8 met dt=0.01
print("error bij t=8 met stap dt=0.01:",np.round(c3*10**3,3),"mm")

dt = 1e-4
t = np.linspace(t0, t1, int(1+t1/dt))

Pos_num = np.zeros(len(t))
Speed_num = np.zeros(len(t))

Pos_num[0] = 0
Speed_num[0] = v0

for n in range(1, len(t)):
    a = Accelaration(Speed_num[n-1])
    Speed_num[n] = Speed_num[n-1]+a*dt
    Pos_num[n] = Pos_num[n-1] + Speed_num[n-1]*dt

c4 = (16-Pos_num[80000])            #error bij t=8 met dt=1e-4
print("error bij t=8 met stap dt=1e-4:",np.round(c4*10**3,3),"mm")

plt.plot(t,Speed_num, "y--")
plt.plot(t,Pos_num, "r")
plt.plot(Pos_num, Speed_num, "g")
plt.show