Question

Given the Dutch Roll mode approximation for the Convair 880 jet, $\Delta \dot{\beta} = -0.1 \Delta \beta - 600 \Delta r + 21 \Delta \delta_r$, $\Delta \dot{r} = 0.0003 \Delta \beta - 6.1 \Delta r + 0.01 \Delta \delta_a + 0.1 \Delta \delta_r$, 1. Find the Laplace transform of the set of differential equations. Assume zero initial conditions. 2. Obtain the following transfer functions: $\frac{\Delta \beta}{\Delta \delta_r}$, $\frac{\Delta r}{\Delta \delta_a}$

          Given the Dutch Roll mode approximation for the Convair 880 jet,
$\Delta \dot{\beta} = -0.1 \Delta \beta - 600 \Delta r + 21 \Delta \delta_r$,
$\Delta \dot{r} = 0.0003 \Delta \beta - 6.1 \Delta r + 0.01 \Delta \delta_a + 0.1 \Delta \delta_r$,
1. Find the Laplace transform of the set of differential equations. Assume zero initial conditions.
2. Obtain the following transfer functions:
$\frac{\Delta \beta}{\Delta \delta_r}$, $\frac{\Delta r}{\Delta \delta_a}$

Given the Dutch Roll mode approximation for the Convair 880 jet,
Δβ̇ = -0.1 Δβ - 600 Δ r + 21 Δ,
Δṙ = 0.0003 Δβ - 6.1 Δ r + 0.01 Δ + 0.1 Δ,
1. Find the Laplace transform of the set of differential equations. Assume zero initial conditions.
2. Obtain the following transfer functions:
(Δβ)/(Δ), (Δ r)/(Δ)

Added by James M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

07/10/2023

Step 1

The given differential equation is: -0.1-600r+21 r=0.00033-6.1r+0.01+0.1 To find the Laplace transform, we need to take the Laplace transform of each term in the equation. Taking the Laplace transform of the left-hand side: Laplace transform of -0.1: Show more…

Show all steps

Thanks for your feedback!

Texts: Given the Dutch Roll mode approximation for the Convair 880 jet, =-0.1-600r+21 r=0.00033-6.1r+0.01+0.1& (1) (2) 1. Find the Laplace transform of the set of differential equations. Assume zero initial conditions. 2. Obtain the following transfer functions: Ar