I = 1-oa f(x) dx

use matlab

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…

Solve the initial value problem below using the method of Laplace transforms. y"- y' - 30y = 0, y(0) = - 1, y'(0) = 49

ZVA @ e SIM a A moodle1.du.edu.om Solve the second order homogeneous differential equation y " -6y'-7y = 0 with intial values y(0) = 0; y'(0) = 1 %3D Maximum file size: 200MB, maximum number of files: 1 Files II

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…

25.18 The following is an initial-value, second-order differential equation: d²x + (5x) dx + (x + 7) sin (wt) = 0 dt² dt where dx (0) (0) = 1.5 and x(0) = 6 dt Note that w= 1. Decompose the equation into two first-order differential equations. After the decomposition, solve the system from t = 0 to 15 and plot the results of x versus time and dx/dt versus time.

A projectile is launched with a velocity of 100 m/s at an angle of 30° above the horizontal. Create a Simulink model to solve the projectile's equations of motion, where x and y are the horizontal and vertical displacements of the projectile. X=0 x(0) = 100 cos 30º x(0)=0 ÿ=-g y(0)=0 y(0)=100 sin 30º Use the model to plot the projectile's trajectory y versus x for 0≤t≤10 s.

The one-dimensional heat equation ut + a²uxx = 0 is discretised using the forward Euler time scheme and a two node centred spatial scheme. This discretisation results in the following equation un n+1 u = a² u+12u?+ u-1 4x² At • Comment on the linearity, order and type of the partial differential equation. • Check the consistency of the discrete equation and state the order of the truncation error for At and Ax. Using the modified equation method, investigate the stability of the discrete equation. • Comment on any stability limitations in terms of choice of At. • Comment on the implications of this scheme with regards to numerical diffusion and dispersion, if any.

Use Euler's method, with step size, h = 0.1, to approximate the solution at t= 0.3 for the initial value problem dx = =x-t , x(0)=1 dt