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%matplotlib inline

Springs: How do they work?

Introduction

In this investigation, we'll determine how the restoring force of a spring depends on its displacement from equilibrium.

Procedure

Data & Analysis

m (g)	x (cm)
50	.6
100	1.2
150	1.9
200	2.6
250	3.3
300	4
350	4.9
400	5.6



In [39]:

    
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit

#------------------------------
#Write your plot/fit code below
#------------------------------
falcons = [0, 50, 100, 150, 200, 250, 300, 350, 400]
displacement = [0,.6,1.2,1.9,2.6,3.3,4,4.9,5.6]

xx = np.linspace(0,500,10)
def lin_model( x, a, b):
    return a*x + b
a,b = curve_fit(lin_model, falcons, displacement)[0]
print(a,b)
plt.title('')
plt.ylabel ('distance (cm)')
plt.xlabel ('weight (g)')
plt.plot(xx, lin_model(xx, a, b))
plt.plot(falcons,displacement,'.')









    



0.0140999999978 -0.142222222225






    Out[39]:





[<matplotlib.lines.Line2D at 0x9199080>]

$$y=0.0140999999978x-0.142222222225$$

Results

Our experiment shows the amount of weight put on a string is proportional to how much it is displaced. We yielded an equation where the relation between weight and distance is linear, which was $y=0.014098x−0.142$.



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