Question 14 Solve the given differential equation (where the function is subject to the given conditions) by using Laplace transforms. y" + 2y' = 0, y (0) = 0, y' (0) = 2 (A) y = 1- e 2t -2t (B) y = 1-e 2 © y = 1+e 2t D There is no correct answer among the choices. E) y = -e 2t
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- In this exercise we show that in the general case, exact recovery of a linear compression scheme is impossible. a. Let A ∈ Rn,d be anarbitrary compression matrix where n ≤ d−1. Show that there exists u,v ∈ Rd,u= v, such that Au = Av. Hint: Show that there exists u= 0,v = 0 such that Au = Av = 0. Hint: Consider using the rank-nullity theorem. b. Conclude that exact recovery of a linear compression scheme is impossible.laplace transformsole using laplace transforms Do not answer in image format
- Derive the governing differential equation for each system with the chosen generalized coordinate. SEE THE IMAGE BELOW Answers: 1. GDE: (5/2) mẍ + (5/4) kx = 0 2. GDE: (7/48) mL² ϴ [note: theta symbol has two dots above) + (3/8) cL² ϴ [ note: theta symbol has one dot above] + 5 kL² ϴ = 0Vibrations Question The following mass–spring system is sliding on a surface of kinetic friction.The system has the following parameters for initial design purposes subject to changes based on overall system performancem=100 kg, k=1300 N/m , x(0)=0.4 , v(0)-0.01, uk=0.08, F(t)=01. Obtain the equation of motion of the system2. Derive the equivalent first-order ODEs with initial conditions to represent part 1Knowing that u c(t) it is the unit step function, the inverse Laplace Transform of the function F(s)= e-s(s-2)/s2 - 4s +3 is: a) f(t) = u1(t) e2(t-1) cosh(t - 1) b) f(t) = u1(t) e2(t-1) cosh(t) c) None of the answers d) f(t) = u2(t) e2(t-1) cosh(t - 1) e) f(t) = u2(t) e2(t-1) cosh(t - 2)
- #4 The life of an automotive component can be modelled by a Weibull distribution. Calculate F(t) R(t) h(t) at the end of rotating period of 36,000 milesA velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
- I don't understand how to solve this problem I think I am getting an arithmatic error but I am unsure.Response using Laplace transformation.The Laws of Physics are written for a Lagrangian system, a well-defined system which we follow around – we will refer to this as a control system (CSys). For our engineering problems we are more interested in an Eulerian system where we have a fixed control volume, CV, (like a pipe or a room) and matter can flow into or out of the CV. We previously derived the material or substantial derivative which is the differential transformation for properties which are functions of x,y,z, t. We now introduce the Reynold’s Transport Theorem (RTT) which gives the transformation for a macroscopic finite size CV. At any instant in time the material inside a control volume can be identified as a control System and we could then follow this System as it leaves the control volume and flows along streamlines by a Lagrangian analysis. RTT:DBsys/Dt = ∂/∂t ʃCV (ρb dVol) + ʃCS ρbV•n dA; uses the RTT to apply the laws for conservation of mass, momentum (Newton's Law), and energy (1st Law of…