1. Consider the initial value problem ü(t)+yü(t)+u(t)=0; u(t=0)=2, ú(t = 0) = 0. For a given y, say y = 0.25, graph the

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1 Consider The Initial Value Problem U T Yu T U T 0 U T 0 2 U T 0 0 For A Given Y Say Y 0 25 Graph The 1 (75.93 KiB) Viewed 67 times

1. Consider the initial value problem ü(t)+yü(t)+u(t)=0; u(t=0)=2, ú(t = 0) = 0. For a given y, say y = 0.25, graph the solution and determine the time t at which the solution becomes "negligible." Interpret the word “negligible” in a way consistent with the resolution of your graph. Repeat this process for other values ofy in the interval 0 <y<2. Construct a graph of t versus y by plotting the values you have found. Finally, determine an analytical formula for the dependence of t on y.