
Yefim S. answered 07/21/20
Math Tutor with Experience
L-1{s2/(s2 + 1)2} = L-1{s/(s2 + 1)} • L-1{s/(s2 + 1)} = cost • cost = ∫0tcosvcos(t - v)dv = 1/2∫0t(cost + cos(2v - t))dv = 1/2(vcost + 1/2sin(2v - t))0t = 1/2tcost + 1/4sint - 1/4sin(-t) = 1/2(tcost + sint);
here • is convolution sign.