3. You should also recall from the last homework this model of an accelerometer. mass Ht,...
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)
Q20. (a) Describe the differential equation (3) d'y(r)_ydytr) dx dx [6 marks] (b) Apply the Laplace transform to equation (3) below and express the Y(s)-L{y(x)) in s-domain when μ4-YQ . function [14 marks] (c) Apply partial fraction decomposition upon the following system so that the denominator becomes of second order. G, (s) s4-81 [12 marks] (d) Consider the following transfer function. G,(s) (i) Find the function in time domain by applying the inverse Laplace transform on equation (5); assume zero...
Question: given a differential equation: a. initial conditions for the plan and input are zero, derive plan's transfer function in Laplace transform b. using inverse Laplace transform, find the solution for the differential equation for the plan (find function y(t)). c. derive state-space model of the plan d. Assume open-loop system with no controller added to the plant, analyse the steady-state value of the system using final value theorem and step input e. Calculate value of the overshoot, rise time...
Question No.2 (CLO 21 10 marks) ) In the circuit shown the input v(O) is a step voltage of sv and the output is the voltage across the capacitor vot) a. Find the output voltage in Laplace domain. Find the output voltage as a function of time (assume the initial voltage across the capacitor is zero). Sketch the output voltage. Find the time constant and settling time. . c. (b) Given the following system G (s)-=-: i Find the differential...
A damped forced oscillation with mass-spring sys- tem is modeled as an nonhomogeneous ODE as following: my" + cy' + ky = r(t) where m = 1 kg, k = 1 N/m and c = 2 N m/s. Initially, y(0) 1m y(0) = -1m/s. r(t) is the input force for this system. Initially (t = (s), there is no input force for this system r(t) = 0 N. At time t = 2s, a costant force (r(t) = 2 N)...
please solve number 2 and number 4 from the following picture. 2. The equivalent s-domain model for an RC circuit is shown below. w The loop equation in the s-domain is given by: 3165) + 16 = 3244 Determine the current i(t). Use the phase shift approach. 3. Determine the inverse Laplace transform of s? Y(s) - 10s +3[sY(s) - 10 ] + 2Y(s) = - 4. Clearly answer the following questions: a. Explain the purpose of using the Laplace...
s) Given the following rotational mechanical system, hot relates the input variable T (applied torque) to the output a) Write the differential equation that re variable angular displacement) b) Convert the differential equatio c) Write the Transfer function of the system (I. w ent the differential equation to Laplace domain assuming initial conditions Zero Consider the following values for the parameters: J - 2 kg-m? (moment of inertial of the mass) D = 0.5 N-m-s/rad (coefficient of friction) K-1 N-m/rad...
The state space model of an interconnected three tank water storage system is given by the following equation: -3 1 0 1rh dt os lo 0 3] 10 1-3 The heights of water in the tanks are, respectively, h,h2,h3. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qǐ1,W2,4a. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks...
please help. Note: u(t) is unit-step function Consider the system with the differential equation: dyt) + 2 dy(t) + 2y(t) = dr(t) – r(e) dt2 dt where r(t) is input and y(t) is output. 1. Find the transfer function of the system. Note that transfer function is Laplace transform ratio of input and output under the assumption that all initial conditions are zero. 2. Find the impulse response of the system. 3. Find the unit step response of the system...
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to a unit step input u(t) is known to be input of u(t) and an output of y(t). The forced response portion 1 Ys) (3 +3s2+ 4s +5) = a) Determine the input-output differential equation for the system b) From your result in a), determine the transformed free response Yee (s) corresponding to initial conditions of: y(0)= y(0) = 0 and ý(0)-6 Part B (20pts)...