Tugas rungekutta MFS

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Soalrunge.png

Koding

import numpy as np

m = eval(input('massa benda: '))

g = eval(input('percepatan gravitasi: '))

u = eval(input('koefisien gesek bidang: '))

cd = eval(input('koefisien gesek udara: '))

teta = eval(input('sudut kemiringan bukit: ')) * (np.pi / 180)

sint = np.sin(teta)

cost = np.cos(teta)

v0 = 0

t0 = 0

dt = 1

error = 100

tries = []

p = g * (sint - u * cost)

q = cd / m

def dvdt(t0, v0):

 return p - q * (v0 ** 1.5)

while error > 0.005:

 k1 = dvdt(t0, v0) 
 k2 = dvdt(t0 + 0.5 * dt, v0 + 0.5 * dt * k1)
 k3 = dvdt(t0 + 0.5 * dt, v0 + 0.5 * dt * k2) 
 k4 = dvdt(t0 + dt, v0 + dt * k3) 
 v1 = v0 + (1.0 / 6.0) * (k1 + 2 * k2 + 2 * k3 + k4)
 t0 = t0 + dt
 error = ((v1 - v0) / v1) * 100 
 v0 = v1
 tries.append(v1)
 

t1 = len(tries)

print(f'kecepatan maksimum yang dapat dicapai adalah {round(v1, 2)} m/s dengan waktu {t1 + 1} s')

Hasilmfs.png