3. Calculate the response of the underdamped system given by using the Laplace transform method. ...
1. [5 pts] Unilateral Laplace Transform. Use the unilateral Laplace transform to determine the response of the system described by the following differential equation with the given inputs and initial conditions:LaTeX: \frac{\rm d}{ {\rm d} t } y(t) + \ 10y(t) = \ 10x(t), d d t y ( t ) + 10 y ( t ) = 10 x ( t ) , LaTeX: y(0^-) = 1, x(t) u(t) = u(t). y ( 0 − ) = 1 ,...
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...
Write the equation of motion and Laplace transform for the following system knowing that Assume zero initial conditions.
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)
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...
4. Solve the given differential equation (i.e., find y(t)) using Laplace transform method: and subject to the conditions that yo) = 0 and y” + 2y'+y=0 y’0) = -2. 21
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t) cannot be computed...
Solve the following initial value problem using the Laplace transform method: y' + 8y = -3, y(0) = -5.
Solve each of the following differential equations using the Laplace Transform approach and plot the response of the system to the given change in u(). (Linearize where necessary) dy ch + 2 t-0
Given an underdamped single-degree-of-freedom system with m 10 kg. c = 20 Ns/m. k = 4000 N/m. Assuming zero initial conditions Xo-Xo-0. response of the system to a unit step function f(t) - 1. itcx +Kx) steady-state value of the unit step response.