1. Find the Laplace transforms of (a) t°sinat (b)te" sin3t (c) cosat – cos bt (d) +tsinat t 1-cost (g) cos 2t - cos3t sint sin5t -+tsint t t t 2. Use the Laplace transform of the second derivative to derive the transformation a (a) L{sinhat}: s² –a² (b)L{coshat} = s² -a? o 3. Evaluate (a) ſte * sint dt cosat – cos bt dt e sint dt (c). t sin?t dt (e) -2t sinht dt coi cos 6t – cos 4t dt t t t 4. Find the Laplace transform from the following diagram 1 -1F 2.

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