Honors MP - Answers
Name: _________________________________ NetID:
_____________________ Section#: ______
Part 1: Monte Carlo
1. Write the Matlab command using 'vol' to compute the volume of the
ellipse using 1000 points.
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2. What is the result from above?
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3. Rerun the command in (1) with 10,000 and then 100,000 points
and write down the results.
___________________________
___________________________
4.Compare these results with the actual volume. When we increase
the number of points does the accuracy improve in general?
Explain your answer. (Hint: research the expression "The Law of
Large Numbers"
_________________________________________________________________________________________________________
Part 3: Harmonic Oscillator
1. Based on the ODE equation stated in the instructions write the
ODE as a system of two equations:
Don't write Matlab code, just write the math form
of the equations.
dx/dt =
____________________________________________________________________
dv/dt =
____________________________________________________________________
2. Now run your code by typing in the following ( after you have
filled in the blanks). See step 3 Refine, Generalize, ... to get the
values.
>> [t , xv ] = ode45(
@xvprime , _________________________,
____________________________ )
3. Fill in the blank to plot x versus time.
>> plot( t ,
_________________________________ )
4. Fill in this blank ____________________ to indicate which
of the cases
a. m = 1, k =
100, b = 2
b. m =
1, k = 100, b = 20
c. m =
1, k = 100, b = 5
matches the plot below.
After answering the above questions, you must email your answers and
attach the files:
inEllipse.m
update.m
velocities.fig
xvprime.m