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philosphy111of

Answered question

2021-11-21

Required information
An LTI system has an impulse response

g (t) = 5 e^{- 3} u (t)

Find the numerical value of

y (t) a t t = 0.6

.
The numerical value of

y (t) a t t = 0.6

is ?

James Etheridge

Beginner2021-11-22Added 16 answers

Step 1
The given impulse response

h (t) = 5 e^{- 3 t} u (t)

Take Inverse Laplace

H (s) = \frac{5}{s + 3}

Step 2

y (t) = h (t) \cdot u (t)

Convert in s domain

Y (s) = H (s) U (s)

Y (s) = \frac{5}{s (s + 3)}

Take partial fractions

Y (s) = \frac{\frac{5}{3}}{s} + \frac{- \frac{5}{3}}{s + 3} = \frac{5}{3} (\frac{1}{s} - \frac{1}{s + 3})

y (t) = \frac{5}{3} (1 - e^{- 3 t})

y (0.6) = \frac{5}{3} (1 - e^{- 3 \times 0.6} = 1.4

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