PART D: Systems of ODEs (5 marks) Question Seven: (5 marks) Find the solution of the following system of Differential Equa tions using the Laplace transform. PART D: Systems of ODEs (5 marks) Qu...
Question 4. Consider the system a) b) c) d) Find the Laplace transform of the differential equation with zero initial condition Show that the system has a pole at s-1 Find the zeros of the system Derive state space model of the system in the first canonical form
Question 4. Consider the system a) b) c) d) Find the Laplace transform of the differential equation with zero initial condition Show that the system has a pole at s-1 Find the...
Question. Systems of ODEs of higher order can be solved by the Laplace transform method. As an important application, typical of many similar mechanical systems, consider coupled vibrating masses on springs. Wrovov The mechanical system in the Figure consists of two bodies of mass 1 on three springs of the same spring constant k and of negligibly small masses of the springs. Also damping is assumed to be practically zero. Then the model of the physical system is the system...
Question 2: (26 marks) 2.1 Find the The Laplace transform of the following function t, if 03t<1 2t, if t1 [3] 2.2 Find the inverse Laplace transform of 10e 2 52 - 53 +632 - 25 + 5 (10] 2.3 Find y(4) if y(t) = u(t){t - 2)2 - us(t)/(t - 3) - 2) - us(t)e' (51 2.4 Solve the following initial value problem given by y" + 4y = 28.(t) (0)=1/(0) = 0 181 Question 3: (17 marks) Let...
Use the Laplace transform to find the solution to the differential equation y'' + y = U(t − 1), y(0) = 1, y' (0) = 0. Describe the physical system that this differential equation represents. Plot your solution.
d) Find the Laplace transform of the following function: f (t = 0 to +09) eat dt e) Find the equivalent solution of (d) using MATLAB method(s) (find 2 methods).
d) Find the Laplace transform of the following function: f (t = 0 to +09) eat dt e) Find the equivalent solution of (d) using MATLAB method(s) (find 2 methods).
Question (2): Laplace Transformsa) Find the Laplace Transform of the following using the Laplace Transform table provided in the back:$$ f(t)=\frac{1}{4}\left(3 e^{-2 t}-8 e^{-4 t}+9 e^{-6 t}\right) u(t) $$b) Find the inverse Laplace Transform \(F(s)\) of the following function \(f(t)\) using the table:$$ f(t)=\frac{12 s^{2}(s+1)}{\left(8 s^{2}+5 s+800\right)(s+5)^{2}(10 s+8)} $$
Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system of ODE using Laplace transform method: Xy-=5x1-2x2 + Mu(t-1) x2-=-2x1 + 2x2 x,(t) and x2(t) refer to the motions of the two masses. Consider these initial conditions: x1 (0) = 1, x; (0)-0, x2(0) = 3, x(0) 0
Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system...
2-Using the Laplace transform find the solution for the following equation d/ at y(t)) + y(t) = f(t) with initial conditions y(0 b Hint. Convolution Dy(0) = a
2-Using the Laplace transform find the solution for the following equation d/ at y(t)) + y(t) = f(t) with initial conditions y(0 b Hint. Convolution Dy(0) = a
[URGENT QUESTION]
3. (15 marks) Find the Laplace transform of the following functions (a) a(t) = tfu(t) – ult - 4)) + 4ult - 4). (b) y(t) = x(2t), where x(t) is the function in part 3a
Find the solution for the following differential equation using Laplace transforms: x - x-6x-0, where x(0)-6, x(0) 13 Find the inverse Laplace Transform of the following equation: 547 s2 +8s +25 x(s) =