Mechanical BE (Mathematics-I)

MATHEMATICS-I

125

Example 5 If

1 L  f (t )  e s

1 s

L et f (3t ) 

, prove that

3 ( s 1)

e . ( s  1)

Solution

1 1 L  f (t )  e s  F (s) s t  L e f (3t )  L  f (3t )ss 1 Given

By change of scale property,

L  f (at )  3

1 F ( s / a) a

3

1 3e s e s   L  f (3t )  3 s s 3

e ( s 1)  L et f (3t )  s 1 Example 6 If

 sin t   sin at  1 1 L   tan (1/ s) then prove that L    tan (a / s). t t    

We know by the change of scale property If

L  f (t )  F (s)thenL  f (at ) 

Given

1 F (s / a) a

 sin t  1 L   tan (1/ s)  t  1 1 a  sin at  1 1 L )  tan 1 ( )   tan ( s/a a s  at  a  sin at  1 a L    tan ( ) s  t 

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