Hi Haseeb Khan. You can solve this question using Partial Fraction Method. You can watch next video under this playlist for the same. th-cam.com/video/iWvu4-OoqoY/w-d-xo.html
Given: s^2/((s^2 + 49)*(s^2 + 36)) Set up partial fractions. Two irreducible quadratics with an arbitrary linear expression on top of each one: (A*s + B)/(s^2 + 49) + (C*s + D)/(s^2 + 36) = s^2/((s^2 + 49)*(s^2 + 36)) Multiply to clear denominators: (A*s + B)*(s^2 + 36) + (C*s + D)*(s^2 + 49) = s^2 Expand & Gather: (A + C)*s^3 + (B + D)*s^2 + (36*A + 49*C)*s2 + 36*B + 49*D = s^2 Equate coefficients: A + C = 0 B + D = 1 36*A + 49*C = 0 36*B + 49*D = 0 Solution: A = 0, B = 49/13, C = 0, D = -36/13 Result: 49/13/(s^2 + 49) - 36/13/(s^2 + 36) Arrange each term so that it matches the Laplace transform of sine, thus having 7 and 6 in the numerator respectively; 7/13 * 7/(s^2 + 49) - 6/13 * 6/(s^2 + 36) Take inverse Laplace: 7/13*sin(7*t) - 6/13*sin(6*t)
You can watch same video in Hindi here: th-cam.com/video/dh4-c6RSpOo/w-d-xo.html
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ধন্যবাদ
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1/s(quep) laplans invers kya hoga
mam 1/2s(s_3) ka inverse Laplace transform bta dy plz
Hi Haseeb Khan. You can solve this question using Partial Fraction Method. You can watch next video under this playlist for the same.
th-cam.com/video/iWvu4-OoqoY/w-d-xo.html
@@engineeringclassesbymonika8256 thnks
Mam can you solve s^2/(s^2+49)(s^2+36)
Given:
s^2/((s^2 + 49)*(s^2 + 36))
Set up partial fractions. Two irreducible quadratics with an arbitrary linear expression on top of each one:
(A*s + B)/(s^2 + 49) + (C*s + D)/(s^2 + 36) = s^2/((s^2 + 49)*(s^2 + 36))
Multiply to clear denominators:
(A*s + B)*(s^2 + 36) + (C*s + D)*(s^2 + 49) = s^2
Expand & Gather:
(A + C)*s^3 + (B + D)*s^2 + (36*A + 49*C)*s2 + 36*B + 49*D = s^2
Equate coefficients:
A + C = 0
B + D = 1
36*A + 49*C = 0
36*B + 49*D = 0
Solution:
A = 0, B = 49/13, C = 0, D = -36/13
Result:
49/13/(s^2 + 49) - 36/13/(s^2 + 36)
Arrange each term so that it matches the Laplace transform of sine, thus having 7 and 6 in the numerator respectively;
7/13 * 7/(s^2 + 49) - 6/13 * 6/(s^2 + 36)
Take inverse Laplace:
7/13*sin(7*t) - 6/13*sin(6*t)
Substitute s square = x
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