SOLVED: (a) Find the Laplace transform off() = e"u(t - 1), where u(t 1) denotes the Heaviside step function (b) Find the inverse Laplace transform of[4]F(s) 82 48 8[9]Use Laplace transforms to solve the ordinary differential equationdt dt2 81 = 6(t #),where a(tis the Dirac delta function with initial conditionsI(0) = 12 (0) = Hint: Your result from part (b) may be useful:[12]
SOLVED: (a) Find the Laplace transform off() = e"u(t - 1), where u(t 1) denotes the Heaviside step function (b) Find the inverse Laplace transform of[4]F(s) 82 48 8[9]Use Laplace transforms to solve the ordinary differential equationdt dt2 81 = 6(t #),where a(tis the Dirac delta function with initial conditionsI(0) = 12 (0) = Hint: Your result from part (b) may be useful:[12]
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