Find the inverse Laplace transform of the equation...

Transcript

00:01 Here we need to find out the inverse laplace for y of s which is equal to which is given as 7 s minus 1 over s minus 1 s plus 2 s minus 3 now first of all using partial fraction we can write this as a over s minus 1 plus b over s plus 2 plus c over s minus 3 now taking the lcm so this will be s minus 1 s plus 2 s minus 3 and in numerator we will have a into s plus 2 into s minus 3 plus b into s minus 1 into s minus 3 plus c into s minus 1 into s plus 2 so this will be s square plus 2 s minus 3 s so this will be minus s minus 6 plus b into s square minus s minus 3 s so minus 4 s plus 3 and c into s square this will be minus s plus 2 s so plus s minus 2 divided by s minus 1 s plus 2 s minus 3 now we have the coefficient of s square which will be a plus b plus c coefficient of s will be minus a minus 4 b plus c and the constant term will be minus 6 a plus 3 b minus 2 c divided by s minus 1 s plus 2 s minus 3 and on the left hand side we have 7 s minus 1 over s minus 1 s plus 2 s minus 3 so on comparing the numerators we can see that on the left hand side.

02:17 We don't have a square term so the coefficient of s square that is a plus b plus c will be equal to 0 coefficient of s is 7 so that means minus a minus 4 b plus c will be equal to 7 and the constant term that is minus 6 a plus 3 b minus 2 c will be equal to minus 1 now from here we will get that c is equal to 7 plus a plus 4 b putting this value here this will become a plus b plus 7 plus a plus 4 b equal to 0 that means this will be 2 a plus 4 b plus 7 is equal to 0 similarly, this will be minus 6 a plus this is equal to 4.

03:11 This is equal to 3 b.

03:15 This is 3 this is 3 b minus 2 into 7 plus a plus 4 b on equal to minus 1 on simplifying this will be equal to 8 a plus 5 b is equal to 13 plus 13 equal to 0 now we have these two equations on solving these two equations...

Question

Find the inverse Laplace transform of the equation below $X(s) = \frac{s-1}{s^2 + 3s + 2}$

Question

Find the inverse Laplace transform of the equation below $X(s) = \frac{s-1}{s^2 + 3s + 2}$

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