( 1 point ) Take the Laplace transform of the following initial value and solve for * ( S ) = [ Ly (D )1 : *" + V = [ sin ( an ) , Ost < 1 10 , * ( D ) = 0 . *’ ( 0 ) = 0 1 5 I * ( S ) = \( pit pien ( – 5 ) / ( ( 5 / 2 + pin 2 ; ( 5 / 2 + 1 ) FEE . Hint : write the right hand side in terms of the Heaviside function . Now find the inverse transform :" * (1 ) = Note : JI 1 1 ( 5 2 + 1 2 ) ( 5 2 + 1) 12 2 – 16 52 + 1 52 + 17 2. ( Notation : write ult – c ) for the Heaviside step function " . ( I ) with step at * = C. )
( 1 point ) Take the Laplace transform of the following initial value and solve for
* ( S ) = [ Ly (D )1 :
*" + V =
[ sin ( an ) , Ost < 1
10 ,
* ( D ) = 0 . *’ ( 0 ) = 0
1 5 I
* ( S ) =
\( pit pien ( – 5 ) / ( ( 5 / 2 + pin 2 ; ( 5 / 2 + 1 )
FEE
. Hint : write the
right hand side in terms of the Heaviside function .
Now find the inverse transform :"
* (1 ) =
Note :
JI
1
1
( 5 2 + 1 2 ) ( 5 2 + 1) 12 2 – 16 52 + 1 52 + 17 2.
( Notation : write ult – c ) for the Heaviside step function " . ( I ) with step at * = C. )
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