CODEWITHSUNDEEP
pythonphysicsnumerical
Karanbir Bains
Karanbir Bains

Reputation: 21

Python numerically solved harmonic oscillator graph generates unwanted results

Ive been trying to numerically solve for the graph of a basic harmonic oscillator but a problem occurs when acceleration on the object is proportional to the inverse of the distance from the centre:

import math
from pylab import *
xg = [2]
xt = [0]
k = 1

dt = 1/1000
Vx = 0
for i in range(800000):
    a = -1/xg[i-1] #acceleration on the object
    Vx = Vx + dt*a
    xg.append(xg[i-1]+Vx*dt)
    xt.append(i*dt)
plot(xt,xg)
show()

As you can see it seems to dip down and not return for some reason.

I am wondering what is causing this to happen, I've been trying to solve this for hours.

Yes, I am new to python, stack exchange and solving problems numerically. Any feedback is appreciated

Upvotes: 2

Views: 2835

Answers (2)

rudy
rudy

Reputation: 196

Assuming you want an acceleration proportional to the inverse of the distance, the numerical values will diverge when xg is near 0, inducing numerical instability.

Upvotes: 0

Anthonydouc
Anthonydouc

Reputation: 3364

Try this instead

import math
from pylab import *
xt = [2]
t = [0]
k = 1

dt = 0.0001
Vx = 0
for i in range(800000):
    t.append(dt*i)
    a = -k*xt[i]
    xt.append(xt[i] + dt*Vx)
    Vx = Vx + dt*a
plot(t,xt)
show()

You end up with this: (I also decreased the time step fyi to 1/10000) enter image description here

Upvotes: 2

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