Problem 1
Iaplnce traneform of \((t \sin t)=\). .
Problem 8
\(L^{-1}\left[\frac{x}{(2 s+3)^{2}}\right]=\ldots\)
Problem 18
\(L^{-1}\left\\{\frac{1}{(s+3)^{5}}\right\\}=4 \ldots\)
Problem 29
\(L^{-1}\left\\{\frac{1}{(s+3)}\right\\}=\ldots \ldots\)
Problem 31
If \(L^{-1}\left\\{\frac{c}{(s+1)^{2}}\right\\}=\frac{t \sin t}{2}\) then \(L^{-1}\left\\{\frac{8 s}{\left(4 s^{2}+1\right)^{2}}\right\\}\)
Problem 34
Laplace transform of \(\dot{t}^{4}\) erut is (i) \(\frac{41}{(a+a)^{4}}\) (ii) \(\frac{4 t}{(s+a)^{5}}\) (iii) \(\frac{4 !}{(s-a)^{4}}\) (ip) \(\frac{51}{(s-a)^{5}}\)
Problem 36
\begin{aligned} &L^{-1} \frac{s^{2}}{\left(s^{2}+4\right)^{2}} \text { is }\\\ &\text { (w) } \frac{1}{2} \sin 2 t+\frac{t}{4} \cos 2 t \text {. } \end{aligned}
Problem 37
\(L^{-1} \frac{1}{s\left(s^{2}+1\right)}\) is (i) \(1+\sin t\) (ii) \(1-\sin t\) (iut) \(1+\mathrm{mos}\) (io) \(1-\cos t\).
Problem 38
L \([u(t-a) \mid\) where \(u(t-a)\) is a unit step function, is (i) \(\frac{e^{-a x}}{s}\) (ii) \(\frac{e^{a n}}{a_{i}}\) (iii) \(\frac{e^{-a t}}{s^{2}}\) (iv) \(\frac{e^{a i}}{s^{2}}\).
