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Find impulse response of the following equation,d2y(t)dt2+5dy(t)dt+6y(t)=x(t)
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written 2.3 years ago by |
Solution:
d2y(t)dt2+5dy(t)dt+6y(t)=x(t)
Applying Laplace transform of the given equation,
S2Y(S)+5SY(S)+6Y(S)=X(S)Y(S)(S2+5S+6)=X(S)
Transfer function H(S)=Y(S)X(S)=1(S2+5S+6)
H(S)=Y(S)=1S2+5S+6
H(S)=1(S+3)(S+2)=AS+3+BS+21=A(S+2)+B(S+3)
∴H(S)=−1S+3+1S+2
Applying Inverse Laplace transform,
h(t)=−e−3tu(t)+e−2tu(t)