Question

2. Consider a system governed by the following differential equation: $2\dot{y}(t) + 4y(t) = 4x(t)$, with zero initial conditions. a) Find its unit step response, $y_s(t)$, and unit ramp response, $y_r(t)$. b) In terms of your answers to part (a) above, write down the response of the above system due to the following input, $x(t)$: $x(t)$ c) Using the final value theorem, find the steady state response (if it exists) of the above system due to the following inputs: i) $x(t) = 4u(t-1)$, ii) $x(t) = 2u(t) + 2r(t)$

          2. Consider a system governed by the following differential equation:
$2\dot{y}(t) + 4y(t) = 4x(t)$, with zero initial conditions.
a) Find its unit step response, $y_s(t)$, and unit ramp response, $y_r(t)$.
b) In terms of your answers to part (a) above, write down the response of the above system due to the
following input, $x(t)$:


$x(t)$

c) Using the final value theorem, find the steady state response (if it exists) of the above system due to the
following inputs:
i) $x(t) = 4u(t-1)$, ii) $x(t) = 2u(t) + 2r(t)$

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2. Consider a system governed by the following differential equation:
2ẏ(t) + 4y(t) = 4x(t), with zero initial conditions.
a) Find its unit step response, ys(t), and unit ramp response, yr(t).
b) In terms of your answers to part (a) above, write down the response of the above system due to the
following input, x(t):

x(t)

c) Using the final value theorem, find the steady state response (if it exists) of the above system due to the
following inputs:
i) x(t) = 4u(t-1), ii) x(t) = 2u(t) + 2r(t)

Added by Diego R.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Hafiz Shahzaib

Step 1

The given differential equation is 2y'' + 4y' = 4x. To solve this, we need to find the complementary function and particular integral. The complementary function is found by assuming y = e^(rt), where r is a constant. Substituting this into the differential Show more…

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please help me urgent 2Co d bywg 2ye+4y=4xwith ro iitiat conditioms .Flind i umif mep response,0, od unit rmp respoe,y bIn tems of your answers to part aabovewrite down the response of the above system due to the following input,xt): c Using the final valuc theorem,find the steady state reponse if it exists of the above system due to the following inputs: x(1=4ut-1it=2(+2r

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