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Unformatted text preview: pick α 1 = α 2 = β 1 = β 2 = 1, and start with any initial populations x and y that are away from the stationary points. 2. Consider the equation of a damped, driven simple harmonic oscillator d 2 y dt 2 + 2 q dy dt + ω 2 y = A cos ωt a) Find the analytical solution for y ( t ), neglecting the homogeneous solution describ-ing transient behavior. b) Write a Fortran 77 or Fortran 90 code that uses the Verlet algorithm to determine y ( t ). Also in your code, compute the analytical solution y ( t ) at each time step for comparison. Determine a suitable time step so that the numerical and analytical solutions agree. Determine the resonant frequency where the amplitude is maximum. Run your simulation at exactly the resonant frequency. Hand in a plot of y ( t ) from your code that includes both the analytical and numerical results. 2...
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- Fall '08
- Trigraph, Lotka–Volterra equation