%matplotlib inline
from modsim import *
plt.style.use('ggplot')

In reality, air resistance prevents the penny from reaching this velocity. At about 20 meters per second, the force of air resistance equals the force of gravity and the penny stops accelerating. As a simplification, let’s assume that the acceleration of the penny is a until the penny reaches 20 meters per second, and then 0 afterwards. What is the total time for the penny to fall 381 meters?

a = 9.80665
termV = 20
totalDisplacement = 381


def displacement(a, v0, v1):
    return (v0 ** 2 + v1 ** 2) / 2 / a


def time(a, v0, v1):
    return (v1 - v0) / a


dToTerm = displacement(a, 0, termV)
tToTerm = time(a, 0, termV)
dLeft = totalDisplacement - tToTerm
tAfterTerm = dLeft / termV
tTot = tToTerm + tAfterTerm
print("It will take %f seconds for the coin to fall" % tTot)

It will take 20.987461 seconds for the coin to fall

Exercise: What happens if you spell the name of a system variable wrong? Edit the previous cell, change the spelling of wellesley, and run the cell again.

from modsim import System

bikeshare = System(olin=10,wellesley=2)
bikeshare.wellesle

>>> >>> Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/lib64/python3.6/site-packages/pandas/core/generic.py", line 3081, in __getattr__
    return object.__getattribute__(self, name)
AttributeError: 'System' object has no attribute 'wellesle'

Exercise: Add a third attribute called babson with initial value 0, and print the state of bikeshare again.

from modsim import System

bikeshare = System(olin=1, wellesley=1, babson=0)
print(bikeshare)

olin         1
wellesley    1
babson       0
dtype: int64

In the cell below, write a few lines of code to move a bike from Wellesley to Olin and plot the updated state.

%matplotlib inline
from modsim import (System, plot, newfig)

bikeshare = System(olin=10, wellesley=10)

newfig()
plot(bikeshare.olin, 'r8-')
plot(bikeshare.wellesley, 'bo-')
bikeshare.olin -= 1
bikeshare.wellesley += 1
plot(bikeshare.olin, 'r8-')
plot(bikeshare.wellesley, 'bo-')

def plot_state():
    plot(bikeshare.olin, 'rs-', label='Olin')
    plot(bikeshare.wellesley, 'bo-', label='Wellesley')

Define a function called bike_to_olin that moves a bike from Wellesley to Olin. Run the new function and print or plot the results to confirm that it works.

def bike_to_olin():
    bikeshare.olin += 1
    bikeshare.wellesley -= 1

newfig()

for _ in range(3):
    plot(bikeshare.olin, 'r8-')
    plot(bikeshare.wellesley, 'bo-')
    bike_to_olin()

The following function definitions start with print statements so they display messages when they run. Run each of these functions (with appropriate arguments) and confirm that they do what you expect.

def move_bike_debug(n):
    print('Running move_bike_debug with argument', n)
    bikeshare.olin -= n
    bikeshare.wellesley += n
    
def bike_to_wellesley_debug():
    print('Running bike_to_wellesley_debug')
    move_bike_debug(1)
    
def bike_to_olin_debug():
    print('Running bike_to_olin_debug')
    move_bike_debug(-1)

move_bike_debug(0)

Running move_bike_debug with argument 0

bike_to_wellesley_debug()

Running bike_to_wellesley_debug
Running move_bike_debug with argument 1

bike_to_olin_debug()

Running bike_to_olin_debug
Running move_bike_debug with argument -1

Change the argument of legend to ‘random string’ and run decorate again. You should get an error message that lists the valid location where you can put the legend.

def decorate():
    legend(loc='a random string')
    label_axes(title='Olin-Wellesley Bikeshare',
               xlabel='Time step (min)',
               ylabel='Number of bikes')

bikeshare = System(olin=10, wellesley=10)
newfig()
plot_state()
bikeshare.olin -= 1
bikeshare.wellesley += 1
plot_state()
decorate()

/usr/lib64/python3.6/site-packages/matplotlib/legend.py:326: UserWarning: Unrecognized location “a rand”. Falling back on “best”; valid locations are best upper right upper left lower left lower right right center left center right lower center upper center center

six.iterkeys(self.codes)))

Write a version of decorate that takes an optional parameter named loc with default value ‘best’. It should pass the value of loc along as an argument to legend. Test your function with different values of loc. You can see the list of legal values here.

def decorate(loc=0):
    legend(loc=loc)
    label_axes(title='Olin-Wellesley Bikeshare',
               xlabel='Time step (min)',
               ylabel='Number of bikes')

bikeshare = System(olin=10, wellesley=10)
newfig()
plot_state()
bikeshare.olin -= 1
bikeshare.wellesley += 1
plot_state()
decorate(1)

def move_bike(n):
    bikeshare.olin -= n
    bikeshare.wellesley += n

def bike_to_wellesley():
    move_bike(1)
  
def bike_to_olin():
    move_bike(-1)

def step(p1=0.5, p2=0.5):
    if flip(p1):
        bike_to_wellesley()

    if flip(p2):
        bike_to_olin()

def run_steps(num_steps, p1, p2):
    for _ in range(num_steps):
        step(p1, p2)
        plot_state()

run_steps(100,0.5,0.5)

run_steps(100, 0.2, 0.8)