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A system is represented by
dy + 2y = 4t u(t) dt
The ramp component in the forced response will be—
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- t u (t)
- 2t u (t)
- 3t u (t)
- 4t u (t)
- t u (t)
Correct Option: B
Given equation
| + 2y = 4t u(t) | |
| dt |
taking Laplace transform of the given equation
sY(s) + 2Y(s) = 4/s2
or
Y (s) [s + 2] = 4/s2
or
Y(s) = 4/s2(s + 2)
or
Y(s) = – (1/s) + (2/s2) + 1/(s + 2)
y(t) = – u(t) + 2tu(t) + e–2t
Here the ramp component in the forced response is 2tu(t). Hence alternative (B) is the correct choice.
