chapter6.page04

chapter6.page04 - t 2 sin at laplace,t,simplify →-2 a a...

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4 1. LAPLACE TRANSFORM METHODS we get b x ( s ) = s 2 ( s - 1)( s 2 +2 s - 3) a 2. Using Mathcad Mathcad can help us in ﬁnd both Laplace transform and inverse Laplace transform. To use Mathcad to ﬁnd Laplace transform, we ﬁrst enter the expres- sion of the function, then press [Shift][Ctrl][.], in the place holder type the key word laplace followed by comma(,) and the variable name. For example, to ﬁnd the Laplace of f ( t ) = t 2 sin( at ), you ﬁrs enter the expression t 2 sin( at ) by typing, t^2*sin(a*t) , then press [Shift][Ctrl][.], and entering keyword laplace followed by comma(,) and t, you will get t 2 sin( at ) laplace,t 8 as 2 ( s 2 + a 2 ) 3 - 2 a ( s 2 + a 2 ) 2 If you want a simpliﬁed result, you type comma(,) after entering the variable name and keyword simplify , so the following input t^2*sin(a*t)[Shift][Ctrl][.]laplace,t,simplify will produce the result
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Unformatted text preview: t 2 sin( at ) laplace,t,simplify → -2 a ( a 2-3 s 2 ) ( s 2 + a 2 ) 3 Similarly, to use Mathcad to ﬁnd inverse Laplace transform, we ﬁrst enter the expression, then press [Shift][Ctrl][.], in the place holder type the key word invlaplace followed by comma(,) and the variable name. For example, to ﬁnd the inverse Laplace of 8 as 2 ( s 2 + a 2 ) 3 , you ﬁrs enter the expression 8 as 2 ( s 2 + a 2 ) 3 as, 8a*s^2/(s^2+a^2)^3 , then press [Shift][Ctrl][.], and entering keyword invlaplace followed by comma(,) and s, and for simplifying the result, by another comma(,) and keyword simplify , we get 8 as 2 ( s 2 + a 2 ) 3 invlaplace,s,simplify → 1 a 2 ± sin( at )-ta cos( at )+ t 2 a 2 sin( at ) ¶...
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