Question: Response x(t) of a system to a forcing function u(t) is determined by the differential equation du 2 +3: + x = 2 +

Response x(t) of a system to a forcing function u(t) is determined

Response x(t) of a system to a forcing function u(t) is determined by the differential equation du 2 +3: + x = 2 + 3u. dt Determine the response of this system to a forcing function u(t) = sin(t) applied at time t = 0, given that the initial conditions are set to x(0) = 1 and x'(0) = -1. dx dx dt dt

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

xt 14 e3t cost 14 e3t sint 12 sint 12 cost The response of a system to any input is defined by its ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Accounting Questions!

A population is modeled by the differential equation dP/dt = 1.2P(1 - P/4200) (a) For what values of P is the population increasing? (b) For what values of P is the population decreasing?

A population is modeled by the differential equation (a) For what values of is the population increasing? (b) For what values of is the population decreasing? (c) What are the equilibrium solutions?...

A system is represented by the differential equation where y = output and u = input. (a) Develop a state variable representation and show that it is a controllable system, (b) Define the state...

Given a mass m, a dashpot constant c, and a spring constant k, Theorem 2 of Section 5.1 implies that the equation has a unique solution for t 0 satisfying given initial conditions x (0) = x 0 ,...

In each of Problems 23-30, a second-order differential equation and its general solution y(x) are given. Determine the constants A and B so as to find a solution of the differential equation that...

3. (10 points) A ball is dropped from rest, and falls in the negative y direction under the force of gravity, together with a drag force +mov,, where a > 0. (a) Use dimensional analysis to find an...

Consider the mechanical system shown in Figure 5.93. The inputs are the force $f_{1}$ applied to the cart and the force $f_{2}$ applied at the tip of the rod. The outputs are the displacement...

An accelerometer attached to an object can be modeled as a mass-damper-spring system, as shown in Figure 5.122. Denote the displacement of the mass relative to the object, the absolute displacement...

Please answer and show all work Problem 3.28 According to Einstein's general theory of relativity, light rays are deflected as they pass by a massive object like the sun. The trajectory of a ray...

Show that I = I 0 e-t/+ is a solution of the differential equation IR + L dl/ dt = 0 where r = L/R and I0 is the current at t = 0.

Kristen Lu purchased a used automobile for $13,600 at the beginning of last year and incurred the following operating costs: The variable operating cost consists of gasoline, oil, tires, maintenance,...

A PM DC motor with torque constant kPM is used to power a hydraulic pump: the pump is a positive displacement type and generates a flow proportional to the pump velocity: qp = kpw The fluid travels...

Bright Manufacturing provided the following information for the month ended March 31: View the information. Prepare the income statement. Revenue: Cost of Goods Sold: Cost of Goods Sold Gross Profit...

6. A U.S. Coast Guard patrole boat leaves Fort Lauderdale at 40 knots (nautical miles per hour) and travels for 5, hours on a course of N 37 E and then changes to a course of N 127 E for 7 hours....

CP8-10-submit in Canvas (round all answers to the nearest dollar) n PV$1 FV$1 PVA FVA 5 6% 0.747258 4.212364 1.338226 5.637093 60 0.50% 0.741372 1.348850 51.725561 69.770031 1. You want to buy a...

Assume a budget for City has been approved and the following information is available: . Estimated inflow from revenue $900,000. Estimated inflow from general long-term debt $100,000. Transfer from...

The following information is for X Company's two products, A and B: Product A Product B Revenue $93,000 $90,000 Total contribution margin $39,990 $37,800 Total fixed costs $24,920 $57,550 Profit...

Using thermodynamic data from Appendix 4, calculate G at 258C for the process: 2SO 2 (g) + O 2 (g) 88n 2SO 3 (g) where all gases are at 1.00 atm pressure. Also calculate DG8 at 258C for this same...

The assumption that in the absence of contrary information a business entity will continue indefinitely is the 1 . 6 points 8 0 2 2 5 - 5 9 Multiple ChoiceGoing concern essumptionPeriodicity...

A random variable X is defined by f X (x) = 4e -8|x| The random variable Y is related to X by Y = 4 + 5X. (a) Determine E[X], E[X 2 ], and 2 x . (b) Determine f Y (y). (c) Determine E[Y], E[Y 2 ],...

Consider a signal-plus-noise process of the form z(t) = A cos 2?(f 0 + f d )t + n(t)? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ??(D.29) where n(t) is given by n(t) = n c (t) cos 2?f 0 t ? n s (t) sin 2?f 0...

Write a computer simulation of the PLL estimation problem. Do this by generating two independent Gaussian random variables to form Z 1 and Z 2 given by (11.196). Thus, for a given (11.201). Call the...

=+a randomly selected cork will conform to specification?

=+b. Using the normal distribution, what is the probability that a single control chart point falls above the UCL in a 3.09-sigma control chart?

=+11. U.S. companies commonly use 3-sigma limits to establish control limits. Some other countries (e.g., Great Britain) use control limits that are 3.09 sigmas from the charts centerline.