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Unformatted text preview: a = ¼, 1, 4 and, as in part a), plot the function ( ) y t for all of these simulations on another graph of y vs. t . c) Find the analytical solution by use of the Laplace transform for arbitrary values of the parameters a and c . Problem #2. Simulate the 2 ndorder ODE 2 2 2 ( 1) d y dy y u t dt dt λ + + =subject to the initial conditions (0) '(0) y y = = . You should note that the time has been scaled such that the natural frequency is ω = 1 ( i.e. , a dimensionless time is used equivalent to τ = ωt ). a) Simulate the equation for the values of the parameter = 0.1, 0.2, 0.4, 0.7, 1.0, 1.5 , and plot the results on a single graph of y vs. t . b) Find the analytical solution by use of the Laplace transform for arbitrary values of the parameter λ ....
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 '07
 Alexander
 Math, Operations Research, Laplace, Fundamental frequency, mathematical model

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