Question: (a) Use Laplace transforms to solve the differential equation given that = 0 and d/dt = 0 when t = 0. (b) Using

(a) Use Laplace transforms to solve the differential equation

d0 +8 dr dt + 160 = sin 2t

given that θ = 0 and dθ/dt = 0 when t = 0.

(b) Using Laplace transforms, solve the simultaneous differential equations

di, dt i + + 2i + 6i = 0 di, dt - 31 = 0

given that i1 = 1, i2 = 0 when t = 0.

d0 +8 dr dt + 160 = sin 2t

Step by Step Solution

★★★★★

3.39 Rating (149 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a b so that is Taking Laplace transform... View full answer

blur-text-image
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 Modern Engineering Mathematics Questions!

Q:

a) Write equation of circle with centre (-3, 2) and radius 4. b) Find distance between the points (6,-4) and (3,0). c) What is the value of limx-o Sinx d) Define skew symmetric matrix.

Q:

(a) Obtain the inverse Laplace transforms of (b) Use Laplace transforms to solve the differential equation given that y = 4 and dy/dt = 2, when t = 0. (i) s+ 4 s + 2s + 10 (ii) s-3 (s 1)(S-2) -

Q:

Aves Treats, Incorporated produces birdseeds. All direct materials used in the production process are added at the beginning of the manufacturing process. Labor and overhead are added evenly...

Q:

(a) Use Laplace transforms to solve the differential equation: 2d 2 y/dx 2 +5dy/dx-3y=0, given that when x =0, y=4 and dy/dx=9. (b) In a galvanometer the deflection satisfies the differential...

Q:

Question 5 (11 marks) Consider the system of differential equations d3:_ (it y dy_ ) 393,. (a) Using eigenvalues and eigenvectors, find the real general solution for the system. (1)) Use Laplace...

Q:

Question 4 (30 marks) (a) Given that x(0) =0, y(0) =a, solve the system of differential equations: dx =x+2y+12e" dy -= 4x+3y+18e" di (b) Find the general solution for dx -= x +2x, -3x3 dt dx, -=-5x...

Q:

(a) Given that x(0) =0, y(0) = a, solve the system of differential equations: dx = x+2y+12e" dt dy = 4x+3y+18e" dt (b) Find the general solution for dx1 = x, + 2x, -3x, dt dx2 =-5x, +X2-4x3 dt -2x,...

Q:

Show work for full credit. 4 N/m 40sin3t AWWWW 2 kg 1. (10 pts.) A mass of 2 kg is connected to a spring with a constant of 4 N/m in equilibrium, and is acted on by an external force of 40sin3t N....

Q:

We can also use Laplace transforms to solve n th order differential equations As the simplest example solve the following first order differential equation using the Laplace transform y 0 1 2t y 3y e...

Q:

Solve for Ci using the method of Laplace transforms starting with the differential equations given below . Solve for C(t) and present it in terms of convolutions. Hints: 1. Cp(t) is not given as an...

Q:

To evaluate YoY business performance, the Leadership team of Microsoft Corporation has defined the following financial metrics: Revenue (product vs. services) Gross margin EBITDA Net Debt Calculated...

Q:

Estimate the number of each type of device in use at your campus. Use your universitys Web site to determine the number of colleges, departments, faculty, staff, and students. Make assumptions about...

Q:

Create notes for the following outline: Chapter 5: Accounting for Merchandising Operations 1. Merchandising Activities i. Merchandise ii. Merchandiser iii. Wholesaler iv. retailer b. Reporting income...

Q:

1. What is a channel captain? What is its role in channel cooperation?

Q:

A capillary tube viscometer similar to that shown in Fig. 2.7 is being used to measure the viscosity of an oil having a specific gravity of 0.90. The following data apply: Tube inside diameter = 2.5...

Q:

In a falling-ball viscometer, a steel ball with a diameter of 0.063 in is allowed to fall freely in a heavy fuel oil having a specific gravity of 0.94. Steel weighs 0.283 lb/in 3 . If the ball is...

Q:

A capillary type viscometer similar to that shown in Fig. 2.7 is being used to measure the viscosity of an oil having a specific gravity of 0.90. The following data apply: Tube inside diameter =...

Q:

3.Which of the following is TRUE regarding a classified balance sheet? Group of answer choices A)A classified balance sheet includes both intangible liabilities and long-term liabilities. B)All of...

Q:

Zenith Inc. received an invoice of $4,600 with terms 2/15, n/45. What is the interest rate per year? a. 24.83% b. 2.41% c. 61.22% d. 30.61%

Q:

Recall that on a one-year Treasury security the yield is 5.6100% and 7.5735% on a two-year Treasury security. Suppose the one-year security does not have a maturity risk premium, but the two-year...