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Ii please b) For the following DE, do the following: a) Find the solution in phase...

Question:

b) For the following DE, do the following: a) Find the solution in phase - amplitude form. If we think of each equation as deii please

b) For the following DE, do the following: a) Find the solution in phase - amplitude form. If we think of each equation as describing a linear mass-spring system, determine how often the mass crosses the equilibrium position. Find the time at which the mass first crosses the equilibrium position. Estimate the time for which «(1< 1/100 i) "+4x'+8x = 0; x(0) = 1; x'(0) = 2 x"+2x'+10 x = 0; x(0) = 1; x'(0) = 1 4x"+4 x'+ 13 x = 0; x(0) = -1; x'0) = -1 -x"+ - x'+ - x = 0; x(0) = 2; x'(0) = -1 2 2 2

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Given D e is Given conditions are x 10) = 1 and 10) = 1 2 Consider taxt loro +2D +10) <=0 fenin se The auxiliary on in tim)ventication tion . = -, +342 1 = -1 + 362 30 = 2 = C : , :: El and C = ... 5464) = ēt [ cos (34) + s sincses] : : x (o)= el

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