Question
Let a causal LTI system be governed by the following differential equation y(t) + 1/4 dy/dt = 2x(t), where x(t) and y(t) are the input and output respectively. Its impulse response is
Options :
8e-4tu(t)
8e-1/4tu(t)
2e-4tu(t)
2e-1/4tu(t)
Answer :
8e-4tu(t)
Solution :
Given differential equation is, y(t) + 1/4 dy/dt = 2x(t),
Taking Laplace transform on both sides, we get
y(s) + 1/4 sY(s) = 2X(s)
(s/4+1)Y(s)= 2X(s)
Y(s)/X(s)= 2/(s/4)+1
Y(s)/X(s)= 8/s+4 which is the transfer function of this system.
∴ Impulse response will be, h(t) = L-1 [ 8/s+4] = 8e-4tu(t)
Hence, the correct option is (A).
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