Using the Laplace transform solve mx ″ + cx ′ + kx = 0, x(0) = a, x ′ (0) = b. where m > 0, c > 0, k > 0, and c2 = 4km (system is critically damped). Exercise 6.E. 6.2.6 Solve x ″ + x = u(t − 1) for initial conditions x(0) = 0 and x ′ (0) = 0. Exercise 6.E. 6.2.7 Show the differentiation of the transform property. Suppose L{f(t)} = F(s), then show
Laplace transform of cos t and polynomials. Shifting transform by multiplying function by exponential. Laplace transform of t: L {t} Laplace transform of t^n: L {t^n} Laplace transform of
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