%================================================================
%	(c) Jerome Peter Lynch, (all rights reserved)
%	University of Michigan
%	October 2009
%
%	This program implements a Newmark solution to Problem 2 
%   	in Homework #5.  In particular, the Newmark Linear 
%   	Acceleration method (gamma = 1/2, beta = 1/6)
%================================================================
    %============%
    % PROBLEM #1 %
    %============%

    %Establish Structural Properties
    %===============================
    m  = 1;                      % in kips-s^2/in
    k  = 100;                    % in kips/in
    c  = 0.05*2*sqrt(k*m);       % in kips-s/in
    wn = sqrt(k/m);              % in rad/sec
    Tn = 2*pi/wn;                % in sec
    fn = wn/(2*pi);              % in Hz

    %First Setup Applied Loading
    %===========================
    load('elcentro.mat')
    dt = dt;
    t = t;
    f = -m*Ag*386.4;
    % Note, the vectors Ag (in terms of g), t (in terms of seconds), and 
    % dt (in terms of seconds) are loaded by incovation of this function.
        
    %Apply Newmark Method
    %====================
    gamma = 1/2;
    beta = 1/6;
    [X,Xd,Xdd,t] = newmark(m,c,k,f,dt,gamma,beta,0,0);
	% You need to write a function "newmark.m" that is called right here.
	% The API for the function is provided in a second file.
   
    %Plot Response
    %=============
    figure
    subplot(3,1,1)
    plot(t,X,'-');
    xlabel('Time (sec)');
    ylabel('Displacement (in)');
    title('Response of the Water Tower to El Centro 1940 (NS) Ground Motion')
    
    subplot(3,1,2)
    plot(t,Xd,'-');
    xlabel('Time (sec)');
    ylabel('Velocity (in/s)');
    
    subplot(3,1,3)
    plot(t,Xdd,'-');
    xlabel('Time (sec)');
    ylabel('Acceleration (in/s^2)');
    

    
    
    %============%
    % PROBLEM #2 %
    %============%


%%%%%PROGRAM HERE