Question

[15pt] Consider the following transfer function $X(s) = \frac{\omega_n^2(s+1)}{s^2 + 2\zeta\omega_ns + \omega_n^2}U(s)$, (1) where $\zeta$ and $\omega_n$ are constants. 1. Find the poles and zeros of the transfer function. You should consider expressing the poles in terms of the symbols $\sigma$ and $\omega_d$ we defined in vibrations. 2. Write the ordinary differential equation for the output $x(t)$ with $u(t)$ as input.

          [15pt] Consider the following transfer function
$X(s) = \frac{\omega_n^2(s+1)}{s^2 + 2\zeta\omega_ns + \omega_n^2}U(s)$, (1)
where $\zeta$ and $\omega_n$ are constants.
1. Find the poles and zeros of the transfer function. You should consider expressing the poles
in terms of the symbols $\sigma$ and $\omega_d$ we defined in vibrations.
2. Write the ordinary differential equation for the output $x(t)$ with $u(t)$ as input.

[15pt] Consider the following transfer function
X(s) = (^2(s+1))/(s^2 + 2ζ + ^2)U(s), (1)
where ζ and are constants.
1. Find the poles and zeros of the transfer function. You should consider expressing the poles
in terms of the symbols σ and we defined in vibrations.
2. Write the ordinary differential equation for the output x(t) with u(t) as input.

Added by Adri-N W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Frank Deng

Step 1

For the first transfer function, X(s) = Ï‰n^2(s + 1) U(s) / (s^2 + 2Î¶Ï‰n s + Ï‰n^2), we can see that the numerator has a zero at s = -1 and the denominator has two poles. Show more…

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Consider the following transfer function: X(s) = Ï‰n^2(s + 1) U(s) / (s^2 + 2Î¶Ï‰n s + Ï‰n^2) where Î¶ and Ï‰n are constants. Find the poles and zeros of the transfer function. You should consider expressing the poles in terms of the symbols Ïƒ and Ï‰d we defined in vibrations. Write the ordinary differential equation for the output x(t) with u(t) as input. [15pt] Consider the following transfer function: X(s) = Ï‰^2(s + 1) / -U(s) where Ï‰ and wn are constants. 1. Find the poles and zeros of the transfer function. You should consider expressing the poles in terms of the symbols Ïƒ and Ï‰d we defined in vibrations. 2. Write the ordinary differential equation for the output x(t) with u(t) as input.