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Assignment Description

Need to be done in MATLAB Question (1): 


For this question 1 Part (a) code has been given and not sure if it’s done and need part(b) . So here is the code for part (a) 

%% Script file project1.m

%% Definition of system parameters: global m c k global x0 v0 m = 1e3;     k = 81e3;    % c          x0 = 1;                   

             v0 = 0;        

%% Part (a)

% Plot the time response and total mechanical energy of the SDOF system

% for the different cases of damping being considered.

% Note: Project asks for only the cases of c = [3 18 25]*1e3

% c = 3e3 N.s/m   % under-damped case (zeta = 0.167)

% c = 18e3 N.s/m  % critically damped case (zeta = 1) % c = 25e3 N.s/m  % overdamped case (zeta = 1.389) c_values = [3 18 25]*1e3;


% Plot of the time response figure

for j = 1:length(c_values)     c = c_values(j);

    % plot the free response normalized with respect to x0     fplot(@(t) frsp_sdof(t)/x0, [0,2]), hold on end hold off


% Set plot parameters % set(gca,'FontSize',12) ax = gca; ax.YLim = [-0.8,1]; ax.XTick = (0:0.2:2); ax.YTick = (-0.8:0.2:1); ax.FontSize = 11; ax.LineWidth = 1;

grid, xlabel('t [sec]'), ylabel('x/x_0 (normalized response)') title({'Time history of the free response of a suspension system', ...

    'modeled by a single-degree-of-freedom system'})

LEG = legend('c = 3e3 N-s/m','c = 18e3 N-s/m','c = 25e3 N-s/m'); set(LEG, 'FontSize', 12)


% Plot of the mechanical energy versus time figure

E0 = 0.5*k*x0^2 + 0.5*m*v0^2;  % calculate the initial mechanical energy in


for j = 1:length(c_values)     c = c_values(j);

    vel = derivative(@(t) frsp_sdof(t));  % define the velocity function

    % Define the energy function (E), which is the sum of the potential     % and kinectic energies.  Normalize E w.r.t. the initial energy E0.     E=@(t) (0.5*k*frsp_sdof(t).^2 + 0.5*m*vel(t).^2)/E0;     fplot(E, [0,2]), hold on end hold off


% Set plot parameters ax = gca; ax.YLim = [0,1]; ax.XTick = (0:0.2:2); ax.YTick = (0:0.1:1); ax.FontSize = 11; ax.LineWidth = 1; grid, xlabel('t [sec]'), ylabel('E/E_0 (normalized energy)') title({'Time history of the total mechanical energy', ...

    'of a suspension system modeled by a SDOF system'}) LEG = legend('c = 3e3 N-s/m','c = 18e3 N-s/m','c = 25e3 N-s/m'); set(LEG, 'FontSize', 12)


%% Part (b)



function x = frsp_sdof(t)

% Free response function of a SDOF system global m c k global x0 v0


wn = sqrt(k/m);         % natural frequency ("omega_n") zeta = c/2/sqrt(k*m);   % damping ratio wd = wn*sqrt(1-zeta^2); % damped natural frequency ("omega_d")

  if zeta == 1;     x = x0*exp(-wn*t) + (v0+wn*x0)*t.*exp(-wn*t);  % critically damped case else

    x = exp(-zeta*wn*t).*(x0*cos(wd*t)+(v0+zeta*wn*x0)/wd*sin(wd*t)); end


function df = derivative(f) sym_f = sym(f);

df = matlabFunction(simplify(diff(sym_f)));  % simplify command is optional end


Question (2) 




Question (3): 








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