The differential equation of motion of ship is given by M d2x/dt2 + C dx/dt +...

The differential equation of motion of ship is given by M d2x/dt2 + C dx/dt + Kx = F + F2*exp(-2t). t >0.

when M = 4.8, C = 3, K = 5, F = 3.8, F2 = 3, x(t=0)=1 and dx/dt (t=0)= 1.

Find:

a)the order of X(s) and the number of poles & Find all poles of X(s)

b)Determine the stability of system.

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Solve the differential equation both by undetermined coefficients and the Laplace transform: d2y/dt2– 3 dy/dt +...

Solve the differential equation both by undetermined coefficients and the Laplace transform: d2y/dt2– 3 dy/dt + 2y = 6 exp(3t), y(0) = 6, y’(0) = 14.

Use the Laplace transform to solve the given system of differential equations. dx/dt + 2x +dy/dt=...

Use the Laplace transform to solve the given system of differential equations. dx/dt + 2x +dy/dt= 1 dx/dt− x+ dy/dt− y= e^t x(0) = 0, y(0) = 0

The differential equation for the current in an RLC circuit is given by L d2i/dt2 +R...

The differential equation for the current in an RLC circuit is given by L d2i/dt2 +R di/dt+(1/c)i =wE0 cos(wt) with initial values i(0)=0 and i'(0)=0. Solve the above IVP.

Use the Laplace transform to solve the given system of differential equations. dx/dt + 3x +...

Use the Laplace transform to solve the given system of differential equations. dx/dt + 3x + dy/dt = 1 dx/dt − x + dy/dt − y = e^t x(0) = 0, y(0) = 0

Solve the given system of differential equations by systematic elimination. 2 dx dt − 6x +...

Solve the given system of differential equations by systematic elimination. 2 dx dt − 6x + dy dt = et dx dt − x + dy dt = 3et

1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 =...

1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 = 0 (a) Convert the equation into a first-order system in terms of x and v, where v = dx/dt. (b) Find all of the equilibrium points of the first-order system. (c) Make an accurate sketch of the direction field of the first-order system. (d) Make an accurate sketch of the phase portrait of the first-order system. (e) Briefly describe the behavior of the first-order...

- Populations of birds and insects are modelled by the differential equations dx/dt = 4x −...

- Populations of birds and insects are modelled by the differential equations dx/dt = 4x − 0.2xy and dy/dt = −2y + 0.08xy (a) Which of the variables, x or y, represents the bird population and which represents the insect population? Explain why. (b) Find the equilibrium solutions, and explain their meaning. (c) Find an expression for dy/dx in terms of x and y.

Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y...

Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y Initial conditions: x(0) = 0 y(0) = 2 a) Find the solution to this initial value problem (yes, I know, the text says that the solutions are x(t)= e^3t - e^-t and y(x) = e^3t + e^-t and but I want you to derive these solutions yourself using one of the methods we studied in chapter 4) Work this part out on paper to...

t2 (d2r/dt2) - 9t (dr/dt) + 16r = 4 is an example of a "Cauchy-Euler equation."...

t2 (d2r/dt2) - 9t (dr/dt) + 16r = 4 is an example of a "Cauchy-Euler equation." Such equations appear in a number of physics and engineering applications. a) Write the complementary homogeneous equation. b) Plug r = ekt into the equation you wrote in part a. Show that this solution will not work for any constant k: this equation has no exponential solution. c) Plug the guess r = tn (where n is a constant) into the equation you wrote...

Find the general solution of the given system. dx dt = 6x + y dy dt...

Find the general solution of the given system. dx dt = 6x + y dy dt = −2x + 4y [x(t), y(t)]= _____________, _______________ (6c1+8c2)10sin(6t)+(6c2+8c1)10cos(6t), c1cos(6t)+c2sin(6t) ^above is the answer I got, which is incorrect.

Subjects