# hw1 - t You may simply copy the code already developed to...

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Homework 1 PHZ 5156 Due Thursday September 3, 2009 1. Consider the equation of a simple harmonic oscillator, in this case describing a pendulum of length l in a gravitational ﬁeld g , d 2 θ dt 2 + g l θ = 0 a) Write the second-order linear diﬀerential equation above as two ﬁrst-order dif- ferential equations by introducing a new variable ω which is the angular velocity. Determine the analytical solution for the harmonic oscillator. b) Use the code written in class to apply the Euler and Euler-Cromer methods to compute θ and ω vs. time
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Unformatted text preview: t . You may simply copy the code already developed to learn the basics of Fortran programming and the use of a simple text editor like vi. Compare a plot of θ vs. t over a few periods for the two methods. Also, compare the total energy vs. time computed from the two methods. How well do they compare to the analytical result? How does the computed trajectory depend on the time step Δ t ? Hand in a plot of θ vs. t and energy vs. t computed from both Euler and Euler-Cromer methods. 1...
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