Question Solved1 Answer Find the Laplace transform for the following functions. (a) f(t) = cosa 6t. (b) f(t) = t sinh 3t.

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Transcribed Image Text: Find the Laplace transform for the following functions. (a) f(t) = cosa 6t. (b) f(t) = t sinh 3t.
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Transcribed Image Text: Find the Laplace transform for the following functions. (a) f(t) = cosa 6t. (b) f(t) = t sinh 3t.
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Hello, Qne, (a) E(t)=cos^(2)(6t)Solution(a), L{f(t)}=>L{cos^(2)(6t)}=Using the identity cos^(2)(x)=(1)/(2)+cos(2x)*(1)/(2).=>quad L{(1)/(2)+cos(2*6+1)*(1)/(2)}.=>L{cos^(2)6t}=L{(1)/(2)}+L{(1)/(2)cos(12 t)}=>L{cos^(2)6t}=(1)/(2s)+(1)/(2)(s)/(s^(2)+144))quad({{cos at}=(s)/(s^(2)+a^(2))):}=>L{cos^(2)6t}=(1)/(2s)+(delta)/(2(s^(2)+144))=>L{cos^(2)6+}=(s^(2)+144+s^(2))/(2s(s^(2)+144))=>L{cos^(2)6t}=(2s^(2)+14472) ... See the full answer