Suppose a system is governed by the following differential equation. Linearize this system about 0 0...
Problem 3: Consider the following system governed by the differential equation YOU +370 + 5 + 7420 + 9 y(t) = 11 440 + 13 u (t), where u (t) is the input for the system, and y(t) is the output for the system. a) (30 pts) Use the Laplace transform to derive the transfer function of the system. b) (30 pts) Express the transfer function in the standard form.
A system is described by the following differential equation: Ï + + 4 x = sin(at) The steady-state response can be written: Xss = A sinot + 0) If the phase angle is: JT O = radians 2 What is the excitation frequency, o ? rad 0 = 0 S rad w = 1 S rad 0 = 2 S rad 0 = 4
The motion of a pendulum bob with mass m is governed by the equation mL0" (t) + mg sin θ (t)-0 where L is the length of the pendulum arm, g 3 and θ is the angle (in radians) between the pendulum arm and the vertical. Suppose L 16 ft and the bob is set in motion with (0 1 and 0' (0)--3. Find the second degree Taylor polynomial P2(t) that approximates the angular position θ(t) of the bob near...
Solve in Matlab
Suppose that the position of a falling object is governed by the following differential equation: where c a first-order drag coefficient 12.5 kg/s, m mass 70 kg, and g gravitational acceleration = 9.81 m/s2. Use the shooting method to solve this equation for the boundary conditions: x(0) = 0 x( 12) = 500
Suppose that the position of a falling object is governed by the following differential equation: where c a first-order drag coefficient 12.5 kg/s, m...
Differential Equations
11. Which ordinary differential equation below is equivalent to the following system of linear equations? = -12 t = 3.81 - 12 + cos(t) (a) u" - 3u' +u = cos(t) (b) " +34 +u = -cos(t) (c) " + u' + 3u = -cos(t) (d) " + x - 3u = cos(t)
Rewrite the second order differential equation, as a system of
a first order differential equation. (see picture)
det + sin(a) = 0, 6(0) = el 10) = 0, += [0, 1] 2012 0, t=
1. Find x(s) for the following differential equation. + = sin 3t u(t) x(0) = 0; x'(0) = 0
Assume a dynamic
system is described by the following ordinary differential equation
(ODE)
1. Assume a dynamic system is described by the following ordinary differential equation (ODE): y(4) + 9y(3) + 30ij + 429 + 20y F(t) = where y = (r' y /dt'.. (a) (10 %) Let F(t) = 1 for t 0, please solve the ODE analytically. (b) (10 %) Please give a brief comment to the evolution of the system. (c) (5 %) Please give a brief...
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, ) luWith u(t, 0) u(t,1)-0 for t>0 (boundary conditions) u(o,z)-3 sin(2x)-5 sin(5z) + sin(6z), for O < < 1 (initial conditions) (20 points)
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, )...
4 Linearize the following ODE around Xo 2T,u,-1 0 0 x 2 sin(x) + xu + u2