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2.2. Consider the automobile on an inclined surface described in Problem 1.29 and shown in Figure P1.29. The differential equation is given by $M \frac{dv(t)}{dt} + k_f v(t) = x(t) - Mg \sin\theta(t)$ (a) Compute the response of the velocity model if $x(t) = u(t)$, $v(0) = 0$, and $\theta(t) = u(t)$. (b) Compute the response of the velocity model if $x(t) = u(t - 5)$, $v(0) = 0$, and $\theta(t) = u(t - 5)$. (c) Compute the response of the velocity model if $x(t) = u(t)$, $v(0) = v_0$ and $\theta(t) = \begin{cases} \theta & \text{for } 0 \le t \le 10\\0 & \text{otherwise} \end{cases}$ where $\theta$ is a constant. (d) Compute the step response of the velocity model if $\theta(t)$ is equal to $tu(t) -$ $(t - 10)u(t - 10)$. dataolism of a drug in a human was modeled by

          2.2. Consider the automobile on an inclined surface described in Problem 1.29 and shown in
Figure P1.29. The differential equation is given by
$M \frac{dv(t)}{dt} + k_f v(t) = x(t) - Mg \sin\theta(t)$
(a) Compute the response of the velocity model if $x(t) = u(t)$, $v(0) = 0$, and
$\theta(t) = u(t)$.
(b) Compute the response of the velocity model if $x(t) = u(t - 5)$, $v(0) = 0$, and
$\theta(t) = u(t - 5)$.
(c) Compute the response of the velocity model if $x(t) = u(t)$, $v(0) = v_0$ and
$\theta(t) = \begin{cases} \theta & \text{for } 0 \le t \le 10\\0 & \text{otherwise} \end{cases}$
where $\theta$ is a constant.
(d) Compute the step response of the velocity model if $\theta(t)$ is equal to $tu(t) -$
$(t - 10)u(t - 10)$.
dataolism of a drug in a human was modeled by

2.2. Consider the automobile on an inclined surface described in Problem 1.29 and shown in
Figure P1.29. The differential equation is given by
M (dv(t))/(dt) + kf v(t) = x(t) - Mg sinθ(t)
(a) Compute the response of the velocity model if x(t) = u(t), v(0) = 0, and
θ(t) = u(t).
(b) Compute the response of the velocity model if x(t) = u(t - 5), v(0) = 0, and
θ(t) = u(t - 5).
(c) Compute the response of the velocity model if x(t) = u(t), v(0) = v0 and
θ(t) = θ for 0 ≤ t ≤ 10
0 otherwise
where θ is a constant.
(d) Compute the step response of the velocity model if θ(t) is equal to tu(t) -
(t - 10)u(t - 10).
dataolism of a drug in a human was modeled by

Added by Dustin I.

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