Using Python and the Runge-Kutta 45 method numerically solve the following force-damped harmonic oscillator equation x¨=-2ζω0x˙-ω02x+10sinωt with initial conditions x(0)=1 and x˙(0)=0. In addition, use ζ=110,ω0=10π and ω=ω0 for plot 1 and ω=2ω0 for plot 2 . Note, you will be solving the equation twice, one for a driving force equal to sinw0t and the second with a driving force equal to sin2w0t. h=0.1 and 0≤t≤40 Compare the number of steps used for RK45 with the a Forward Euler Solution using the same level of convergence as the RK45. Plot both solutions and the same graph.
Using Python and the Runge-Kutta 45 method numerically solve the following force-damped harmonic oscillator equation x¨=-2ζω0x˙-ω02x+10sinωt with initial conditions x(0)=1 and x˙(0)=0. In addition, use ζ=110,ω0=10π and ω=ω0 for plot 1 and ω=2ω0 for plot 2 . Note, you will be solving the equation twice, one for a driving force equal to sinw0t and the second with a driving force equal to sin2w0t. h=0.1 and 0≤t≤40 Compare the number of steps used for RK45 with the a Forward Euler Solution using the same level of convergence as the RK45. Plot both solutions and the same graph.
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter14: Numerical Methods
Section14.6: The Trapezoidal Rule
Problem 1E
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Using Python and the Runge-Kutta 45 method numerically solve the following force-damped harmonic oscillator equation
x¨=-2ζω0x˙-ω02x+10sinωt
with initial conditions x(0)=1 and x˙(0)=0. In addition, use ζ=110,ω0=10π
and ω=ω0 for plot 1 and ω=2ω0 for plot 2 . Note, you will be solving the
equation twice, one for a driving force equal to sinw0t and the second with a
driving force equal to sin2w0t.
h=0.1 and 0≤t≤40
Compare the number of steps used for RK45 with the a Forward Euler
Solution using the same level of convergence as the RK45. Plot both
solutions and the same graph.
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