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hw1_solncorrection

# hw1_solncorrection - AE 383 SYSTEM DYNAMICS Correction to...

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AE 383 SYSTEM DYNAMICS Correction to Solution of Homework 1 2-) Find the Laplace transformation of the following time functions: a. f ( t ) = b sin(2 t ) t 0 0 t 3 π/ 2 f ( t ) = u ( t ) sin(2 t ) - u ( t - 3 π/ 2) sin(2 t ) = u ( t ) sin(2 t ) - u ( t - 3 π/ 2) sin[2( t - 3 π/ 2 B ±² ³ a + 3 π/ 2 B ±² ³ b )] = u ( t ) sin(2 t ) - u ( t - 3 π/ 2) { sin[2( t - 3 π/ 2)] a a a a a a A - 1 cos[2(3 π/ 2)] + cos[2( t - 3 π/ 2)] a a a a a a A 0 sin[2(3 π/ 2)] } f ( t ) = u ( t ) sin(2 t ) + u ( t - 3 π/ 2) sin[2( t - 3 π/ 2)] L { f ( t ) } = F ( s ) = 2 s 2 + 4 ´ 1 + e - 3 πs/ 2 µ b. g ( t ) = t + cos(5 t ) 0 t π/ 5 - 2 π/ 5 + t π/ 5 t 4 π/ 5 0 t > 4 π/ 5 g ( t ) = u ( t )[ t + cos(5 t )] - u ( t - π/ 5)[ ± t + cos(5 t )] + u ( t - π/ 5)[ - 2 π/ 5 + ± t ] - u ( t - 4 π/ 5)[ - 2 π/ 5 + t ] = u ( t ) t + u ( t ) cos(5 t ) - u ( t - π/ 5) cos[5( t - π/ 5 B ±² ³ a + π/ 5 B±²³ b )] - u ( t - π/ 5) 2 π 5 - u ( t - 4 π/ 5)( t - 4 π/ 5 + 2 π/ 5) = u ( t ) t + u ( t ) cos(5 t ) - u ( t - π/ 5) { cos[5( t - π/ 5)] a a a a aa A - 1 cos[5( π/ 5)] - sin[5( t - π/ 5)] a a a a aa A 0 sin[5(
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