# coding: utf-8

# Lab 1
# Haley Partlow

# In[1]:

get_ipython().magic(u'matplotlib inline')
import numpy as np
from __future__ import division
import matplotlib.pyplot as plt


# First, determine the frequency of the oscillator using the equation for frequency ${f = (\frac{1}{\lambda})*(\sqrt(\frac{F_{T}}{\mu}))}$

# In[35]:

def Frequency(l,F,m,L):
    f = (1/l)*(F/(m/L))**0.5
    return f


# In[48]:

Wavelength=0.7814 #m
Uncertainty_wavelength=1 #mm
Force=2.45 #N
Uncertainty_Force=0.03 #N
Mass=0.000435 #kg
Uncertainty_Mass=0.000002 #kg
Length=1.555 #m
Uncertainty_Length=0.001 #m

frequency = Frequency(Wavelength, Force, Mass, Length)
print "Frequency = ", frequency, "Hz"


# Second, determine the uncertainty of the frequency using Rule 4 error propagation ${\delta f = f \sqrt{(- \frac{\delta \lambda}{\lambda})^2 + (\frac{1}{2}* \frac{\delta F_{T}}{F_{T}})^2 + (\frac{-1}{2}*\frac{\delta m}{m})^2 + (\frac{1}{2}*\frac{\delta L}{L})^2}}$
#

# In[43]:

def Uncertainty(el,l,eF,F,em,m,eL,L):
    Part1=(-el/l)**2
    Part2=(0.5*(eF/F))**2
    Part3=(-0.5*(em/m))**2
    Part4=(0.5*(eL/L))**2
    ef=(Part1 + Part2 + Part3 + Part4)**0.5
    return ef


# In[55]:

Uncertainty_frequency = Uncertainty(Uncertainty_wavelength,Wavelength,Uncertainty_Force,Force,Uncertainty_Mass,Mass,Uncertainty_Length,Length)
print "deltaf = ", Uncertainty_frequency, "Hz"


# The frequency of the oscillator is 119.77 ${\pm}$ 1.28 Hz.

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