a. Find the Laplace transform of the given function. Use Table 2.2 when applicable.

b. Confirm the result of (a) in MATLAB.

\(t^{2} \sin \left(\frac{1}{2} t\right)\)

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TABLE 2.2 Laplace Transform Pairs No. f(t) F(s) 1 Unit impulse (t) 1 2 1, unit step u,(t) 3 t, unit ramp u,(t) 1/s 1/s 4 8(-a) 5 69 7 8 00 9 u(-a) -1=1,2,... e/s (n-1)!/s" F(a)*/s 1 s+a 1 10 te, n=1, 2,... 1 11 -(e-e"), axb b-a (s+a) n! (s+a)+ 1 (s+a)(s+b) 1 S 12 a-b 1 (ae-be), ab (s+a)(s+b) 1 13 1+ ab a-b -(be -de s(s+a)(s+b) 1 1 14 15 16 16 a (-1+at+e") 1-e-ate) sin of s(s+a) 1 s(s+a) 00 17 cos cof