B solve the ivp in a to obtain the equations of

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Unformatted text preview: tions. (b) Solve the IVP in (a) to obtain the equations of motion. (c) As t → ∞ one part of the solution, the transient term, decays to 0. The term which does not decay, the steady state, is purely oscillatory. By rewriting this term as A sin(kt + φ), identify its amplitude. 2. Find the following transforms: ￿ ￿ (a) L cos 6t + (b) L−1 ￿ s s2 +4 ￿ π 4 ￿￿ 3. Use the definition of the Laplace transform to show that L{eat cos(bt)} = s−a ( s − a) 2 + b 2 4. Use Laplace transforms to solve the following IVPs: (a) y ￿ − 3 y = 2 e − 4t , y (0) = 0 (b) y ￿￿ − 2y ￿ + 10y = 0, y (0) = 1, y ￿ (0) = −3...
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