Write and execute a Matlab function that takes a body\'s mass and velocity and c

Question

Write and execute a Matlab function that takes a body's mass and velocity and calculates the Kinetic Energy of the moving body: KE = 1/2 mV^2 where m is mass in kg and v is velocity in m/sec. Execute the function for at least 5 mass-velocity pairs. Create an Excel spreadsheet with 10 rows of data inputs (mass and velocity). Create a new function that uses the KE function from part a that reads the input data from the spreadsheet, computes the Kinetic Energy, and posts the KE function result to a new column in the spreadsheet. The spreadsheet name can be 'hardcoded' (a fixed value) within your function.

Explanation / Answer

% energy - Program to compute kinetic and potential energy % for a particle acted on by a conservative force clear all; % Clear memory help energy; % Print header %@ Initialize variables kCoeff = 1.0; % Kappa coefficient (N/m) qCoeff = 0.1; % q coefficient (N/m^3) x = input('Enter initial displacement (m): '); v = 0.; % Initial velocity (m/s) mass = 1.0; % Mass of particle dt = 0.05; % Time step (s) KEnergy = 0.5*mass*v^2; % Kinetic energy UEnergy = -0.5*kCoeff*x^2 + qCoeff*x^4; % Potential energy TEnergy = KEnergy + UEnergy; % Initial total energy t = 0; % Time Nstep = 300; % Number of time steps %@ Set up plot of kinetic and potential energy versus time clf; % Clear the figure window figure(gcf); % Bring figure window forward EnergyLimit = 2*abs(TEnergy); % Estimate y-axis limit axis([0, Nstep*dt, -EnergyLimit, EnergyLimit]); % Set axis limits xlabel('Time (s)'); % x-axis label ylabel('Energy (J)'); % y-axis label title('Kinetic (*) Potential (+)'); hold on; % Hold the plot on screen %@ Loop for desired number of steps for istep=1:Nstep %@ Compute kinetic and potential energy KEnergy = 0.5*mass*v^2; % Kinetic energy UEnergy = -0.5*kCoeff*x^2 + qCoeff*x^4; t = (istep-1)*dt; % Time %@ Update the plot by adding new values to the graph plot(t, KEnergy,'r*','EraseMode','none'); plot(t, UEnergy,'b+','EraseMode','none'); while( abs(KEnergy) > EnergyLimit | abs(UEnergy) > EnergyLimit ) EnergyLimit = 2*EnergyLimit; axis([0, Nstep*dt, -EnergyLimit, EnergyLimit]); % Set axis limits end drawnow; % Update the figure now %@ Compute force and acceleration Force = kCoeff*x - 4*qCoeff*x^3; % Force accel = Force/mass; % Acceleration %@ Update position and velocity using Euler-Cromer v = v + accel*dt; % Compute new position and velocity x = x + v*dt; % using Euler-Cromer end

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