quiz3 - L [ t 2 ] = 2 /s 3 . The right hand side is-d ds L...

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Solution for Quiz 3 Find L - 1 " 1 ( s + 1) 3 # . First shifting theorem: L - 1 [ F ( s - a )] = e at L - 1 [ F ( s )] . Here a = - 1, and F ( s - a ) = 1 / ( s +1) 3 , so that F ( s ) = 1 /s 3 . We have L - 1 [1 /s 3 ] = t 2 / 2 . Therefore, L - 1 " 1 ( s + 1) 3 # = e - t 2 t 2 . Check that L [ tf ( t )] = - d ds L [ f ( t )] with f ( t ) = t . The left hand side is L [ tf ( t )] =
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Unformatted text preview: L [ t 2 ] = 2 /s 3 . The right hand side is-d ds L [ f ( t )] =-d ds L [ t ] =-d ds 1 s 2 =--2 s 3 = 2 s 3 . This is equal to the left hand side. 1...
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