Second order differential equations
(b) A second-order differential equation is given as follows:
$$ f^{\prime \prime}(t)-9 f(t)=g(t) $$
where \(g(t)\) is a non-continuous function represented by,
$$ g(t)=5 H(t)+H(t-1) $$
Solve the differential equation using Laplace Transform, if the initial conditions are \(f(0)=0\) and \(f^{\prime}(0)=1\).
Homework Answers
Please assist with the following using Laplace Transform The second order differential equation of a vibratıng...
Please assist with the following using Laplace
Transform
The second order differential equation of a vibratıng system is given by d2 dt'dt 5 1 Determine the system transfer function with initial conditions y(0) y(0)0 5 2 Determine the response of the system, y(t), with a unit step input r(t) and intial conditions y(0)1 and y(0) -1 (15)
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 meth...
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...
Using the Laplace transform, solve the partial differential equation. Please with steps, thanks :) Problem 13: Solving...
Using the Laplace transform, solve the partial differential
equation.
Please with steps, thanks :)
Problem 13: Solving a PDE with the Laplace Transform Using the Laplace transform, solve the equation 山 given the initial and boundary conditions a(x, 0)=1 ifx> 0, u(0, t) -1 if t 2 0.
Problem 13: Solving a PDE with the Laplace Transform Using the Laplace transform, solve the equation 山 given the initial and boundary conditions a(x, 0)=1 ifx> 0, u(0, t) -1 if t...
Problem 3 A system is described by the following second-order linear differential equation d'y dz 5y(sin2t+...
Problem 3 A system is described by the following second-order linear differential equation d'y dz 5y(sin2t+ e-t)u(t) dt2 where y(0)y()0 Solve the differential equation using the Laplace Transform method.
Problem 4. The higher order differential equation and initial conditions are shown as follows: = dy...
Problem 4. The higher order differential equation and initial conditions are shown as follows: = dy dy +y?, y(0) = 1, y'(0) = -1, "(0) = 2 dt3 dt (a) [5pts. Transform the above initial value problem into an equivalent first order differential system, including initial conditions. (b) [2pts.] Express the system and the initial condition in (a) in vector form. (c) [4pts.] Using the second order Runge Kutta method as follows Ū* = Ūi + hĚ(ti, Ūi) h =...
Not yet graded /30 pts Question 3 A system is described by the following second-order linear...
Not yet graded /30 pts Question 3 A system is described by the following second-order linear differential equation dy + +5 6y(t)-4f(t )-3f(t) dt dt2 where y(0)-1. y (0) 5, and the input f(t) e'u(t) Solve the differential equation using the Laplace Transform method. Note that f(0) - 0 Your Answer: no option to upload answers so i emailed them to you Quiz Score: 0 out of 100 hp 12 144 5 6
Not yet graded /30 pts Question 3...
Differential equations 7.4 Operational properties II Formula to use Use operational properties of the Laplace Transform...
Differential equations 7.4 Operational properties II
Formula to use
Use operational properties of the Laplace Transform to determine L{f(x)}, where f(x) is represented in the graph below. Simplify your answer. f(t) 4 1 1 2 3 4 THEOREM 7.4.3 Transform of a Periodic Function If f(t) is piecewise continuous on [0, 0), of exponential order, and periodic with period T, then 1 L{f(t)} es f(t) dt. () di. 1 - e-ST
this is from differential equations. if someone can do the whole sheet except for question 10...
this is from differential
equations. if someone can do the whole sheet except for question 10
if you could do two to of them, I would greatly appreciate it.
thank you in advance.
5. Solve the equation 7" +2+y = 2+32) (do tiot use the Laplace transform.) 6. Use the definition of Laplace transform to find LFO), where f(t) =t if 0 <t<1, () = 1 if IcI<3 and fit -2 ift 3. -1) dx + 3yle" + 1)dy =...
Differential Equations Project - must be completed in Maple 2018 program NEED ALL PARTS OF THE PR...
Differential Equations Project - must be completed in Maple 2018 program NEED ALL PARTS OF THE PROJECT (A - F) In this Maple lab you learn the Maple commands for computing Laplace transforms and inverse Laplace transforms, and using them to solve initial value problems. A. Quite simply, the calling sequence for taking the Laplace transform of a function f(t) and expressing it as a function of a new variable s is laplace(f(t),t,s) . The command for computing the inverse...
Consider the following statements. (i) Given a second-order linear ODE, the method of variation of parameters...
Consider the following statements.
(i) Given a second-order linear ODE, the method of variation of
parameters gives a particular solution in terms of an integral
provided y1 and y2 can be
found.
(ii) The Laplace Transform is an integral transform that turns
the problem of solving constant coefficient ODEs into an algebraic
problem. This transform is particularly useful when it comes to
studying problems arising in applications where the forcing
function in the ODE is piece-wise continuous but not necessarily...
Please assist with the following using Laplace
Transform
The second order differential equation of a vibratıng system is given by d2 dt'dt 5 1 Determine the system transfer function with initial conditions y(0) y(0)0 5 2 Determine the response of the system, y(t), with a unit step input r(t) and intial conditions y(0)1 and y(0) -1 (15)
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...
Using the Laplace transform, solve the partial differential
equation.
Please with steps, thanks :)
Problem 13: Solving a PDE with the Laplace Transform Using the Laplace transform, solve the equation 山 given the initial and boundary conditions a(x, 0)=1 ifx> 0, u(0, t) -1 if t 2 0.
Problem 13: Solving a PDE with the Laplace Transform Using the Laplace transform, solve the equation 山 given the initial and boundary conditions a(x, 0)=1 ifx> 0, u(0, t) -1 if t...
Problem 3 A system is described by the following second-order linear differential equation d'y dz 5y(sin2t+ e-t)u(t) dt2 where y(0)y()0 Solve the differential equation using the Laplace Transform method.
Problem 4. The higher order differential equation and initial conditions are shown as follows: = dy dy +y?, y(0) = 1, y'(0) = -1, "(0) = 2 dt3 dt (a) [5pts. Transform the above initial value problem into an equivalent first order differential system, including initial conditions. (b) [2pts.] Express the system and the initial condition in (a) in vector form. (c) [4pts.] Using the second order Runge Kutta method as follows Ū* = Ūi + hĚ(ti, Ūi) h =...
Not yet graded /30 pts Question 3 A system is described by the following second-order linear differential equation dy + +5 6y(t)-4f(t )-3f(t) dt dt2 where y(0)-1. y (0) 5, and the input f(t) e'u(t) Solve the differential equation using the Laplace Transform method. Note that f(0) - 0 Your Answer: no option to upload answers so i emailed them to you Quiz Score: 0 out of 100 hp 12 144 5 6
Not yet graded /30 pts Question 3...
Differential equations 7.4 Operational properties II
Formula to use
Use operational properties of the Laplace Transform to determine L{f(x)}, where f(x) is represented in the graph below. Simplify your answer. f(t) 4 1 1 2 3 4 THEOREM 7.4.3 Transform of a Periodic Function If f(t) is piecewise continuous on [0, 0), of exponential order, and periodic with period T, then 1 L{f(t)} es f(t) dt. () di. 1 - e-ST
this is from differential
equations. if someone can do the whole sheet except for question 10
if you could do two to of them, I would greatly appreciate it.
thank you in advance.
5. Solve the equation 7" +2+y = 2+32) (do tiot use the Laplace transform.) 6. Use the definition of Laplace transform to find LFO), where f(t) =t if 0 <t<1, () = 1 if IcI<3 and fit -2 ift 3. -1) dx + 3yle" + 1)dy =...
Consider the following statements.
(i) Given a second-order linear ODE, the method of variation of
parameters gives a particular solution in terms of an integral
provided y1 and y2 can be
found.
(ii) The Laplace Transform is an integral transform that turns
the problem of solving constant coefficient ODEs into an algebraic
problem. This transform is particularly useful when it comes to
studying problems arising in applications where the forcing
function in the ODE is piece-wise continuous but not necessarily...
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