Consider the initial value problem with the initial conditions u(0) = u\'(0) = 0
ID: 3081898 • Letter: C
Question
Consider the initial value problem with the initial conditions u(0) = u'(0) = 0. Find the solution to this equation by considering each of the three time intervals separately. In other words, find the solution on the first interval. Then find the solution on the second interval that picks up where the first solution leaves off. Repeat for the third interval. Sketch a graph of your solution. Find the Laplace transform of the following functions. f(t) = pi2t3 - 42 f(t) = t2e-3t g(t) = e2t + 4sin(pit) h(t) = tsin(3t). Recall that cosh(at) = (eat + e-at)/2 and sinh(at) = (eat - e-at)/2. Find the Laplace transform of the following. cosh(at) ebt cosh(at)Explanation / Answer
2. a) laplace transformation of 2*t3 -42 = 62/s4 - 42/s
b) laplace transformation of t2*e(-3t) = 2/(s+3)3
c) laplace transformation of e2t+4sin(t)= 4/(2+s2) + 1/(s-2)
d) laplace transformation of t*sin(3t) = 6s/(s2+9)2
3. a) laplace transformation of cosh(at) = s/(s2-a2)
b) laplace transformation of ebt*cosh(at) = (s-b)'/[(s-b)2-a2]