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Posted: **Thu Jun 02, 2022 9:40 am**

: Table 6 2 Common Laplace Transform Pairs 1 U T S 1 E Cs U T U Tc C 0 S Tnu T N Sn 1 N 1 2 3 8 T 1 1 (63.56 KiB) Viewed 24 times

: Table 6 2 Common Laplace Transform Pairs 1 U T S 1 E Cs U T U Tc C 0 S Tnu T N Sn 1 N 1 2 3 8 T 1 2 (60.23 KiB) Viewed 24 times

TABLE 6.2 Common Laplace Transform Pairs 1 u(t). S 1 e-cs u(t) - u(tc). ,c> 0 S tNu(t)= N! sN+1' N 1, 2, 3, ... 8(t) → 1 8(tc) e, c> 0 1 e-bu(t). s + b' tNe-btu(t) (cos wt)u(t) (sin wt)u(t) >>> (cos² wt)u(t) (sin² wt)u(t). (e-bt → b real or complex N! (s + b) N+¹¹ S → + w² W + w² s² + 2w² s(s² + 4w²) 2w² s(s² + 4w²) 5² 52 به cos wt)u(t) sin wt)u(t) s + b (s + b)² + w² @ (s + b)² + w² 5² w² (s² + ²)² 2ws + ²)² (s + b)² - w² [(s + b)² + w²1² 2w (s + b) [(s + b)² + w²1² (t cos wt)u(t) (t sin wt)u(t)< (te-br cos wt)u(t) (te-bt sin wt)u(t). → N = 1, 2, 3, ... (s² →→→→
6.4. Using the transform pairs in Table 6.2 and the properties of the Laplace transform in Table 6.1, determine the Laplace transform of the following signals: (a) x(t) (e-bt cos²wt)u(t) (b) x(t) = (ebt sin²wt)u(t) (c) x(t) = (t cos²wt)u(t) (t sin²wt)u(t) (d) x (t) = (e) x(t) (cos³wt)u(t) (f) x(t) = (sin³wt)u(t)