Cant seem to plot this correctly using python numpy and matplotlib 1. HARMONIC AND ANHARMONIC OSCILLATORSThis is a modified version of chapter 3 problem 4 in your textbook. For simple harmonic motion, the equation ofmotion is given byd²xdt²=-kxawith a = 1.Write a program that uses the Euler-Cromer method to solve for x(t). For convenience, let a = k = 1. Showthat the period of the oscillations is independent of the amplitude of the motion (this is a key feature of simpleharmonic motion!). Use several different regularly-spaced values of amplitude and show that the amplitudeand period are independent of each other.Write a program that uses the Euler-Cromer method to solve for x(t) when k = 1 but a = 3 and plot arepresentative solution for x(t). Calculate the period of the oscillation for a variety of amplitudes. Show thatthe period of oscillation is now dependent on the amplitude of the motion (this is called anharmonic motion).Describe the anharmonic behavior that you observe. Provide an intuitive, qualitative discussion of why thisbehavior is observed.

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Engineering

Computer Science

Cant seem to plot this correctly using python numpy and matplotlib

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter3: Assignment, Formatting, And Interactive Input

Section3.1: Assignment Operations

Problem 13E

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Cant seem to plot this correctly using python numpy and matplotlib

1. HARMONIC AND ANHARMONIC OSCILLATORS
This is a modified version of chapter 3 problem 4 in your textbook. For simple harmonic motion, the equation of
motion is given by
d²x
dt²
=-kxa
with a = 1.
Write a program that uses the Euler-Cromer method to solve for x(t). For convenience, let a = k = 1. Show
that the period of the oscillations is independent of the amplitude of the motion (this is a key feature of simple
harmonic motion!). Use several different regularly-spaced values of amplitude and show that the amplitude
and period are independent of each other.
Write a program that uses the Euler-Cromer method to solve for x(t) when k = 1 but a = 3 and plot a
representative solution for x(t). Calculate the period of the oscillation for a variety of amplitudes. Show that
the period of oscillation is now dependent on the amplitude of the motion (this is called anharmonic motion).
Describe the anharmonic behavior that you observe. Provide an intuitive, qualitative discussion of why this
behavior is observed.

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