## Instructions

**Objective**

Write a program to solve spring problem in matlab.

## Requirements and Specifications

**Source Code**

```
INTERPO
function df = interpo(t, y, datagm, T)
% Define the critical damping ratio
zeta = 0.02;
% Compute natural frequency
wn = 2*pi/T;
% Define the mass in pounds
m = 1000;
% Compute k
k = wn^2 *m;
% Get variables
x = y(1);
v = y(2);
xg = datagm(t);
df = zeros(2,1);
df(1) = v;
df(2) = -xg - 2*zeta*wn*v - wn^2 *x; % xpp
end
QUESTIONS
clc, clear all, close all
load ELCentro.mat
% Define gravity value
% g = 9.81; % m/s^2
g = 386.08; % in/s^2
% Scale acceleration
fgm = fgm*g;
figure
plot(tgm, fgm), grid on
xlabel('Time (s)')
ylabel('Ground Acceleration $\frac{m}{s^{2}}$', 'interpreter', 'latex', 'fontsize', 18)
%% Question 2
% Interpolate
datagm = griddedInterpolant(tgm, fgm);
%% Question 3: See file interpo.m
%% Question 4
T = 1;
x0 = [0, 1];
[t,y] = ode45(@(t,y)interpo(t,y,datagm,T), tgm, x0);
x = y(:,1);
v = y(:,2);
% Compute acceleration
a = diff(v);
figure
subplot(1,3,1)
plot(t(1:end-1), a), grid on
xlabel('Time (s)')
ylabel('Acceleration $(\frac{in}{s^{2}})$', 'interpreter', 'latex', 'fontsize', 18)
title('Acceleration vs. Time')
subplot(1,3,2)
plot(t, v), grid on
xlabel('Time (s)')
ylabel('Velocity $(\frac{in}{s})$', 'interpreter', 'latex', 'fontsize', 18)
title('Velocity vs. Time')
subplot(1,3,3)
plot(t, x), grid on
xlabel('Time (s)')
ylabel('Displacement $(in)$', 'interpreter', 'latex', 'fontsize', 18)
title('Displacement vs. Time')
%% Question 5
% Now, use different values of T
Ts = 0.1:0.1:3;
% Vectors to store peak values of acceleration, displacement and velocity
accPeaks = zeros(length(Ts),1);
velPeaks = zeros(length(Ts),1);
dispPeaks = zeros(length(Ts),1);
for i = 1:length(Ts)
T = Ts(i);
[t,y] = ode45(@(t,y)interpo(t,y,datagm,T), t, x0);
x = y(:,1);
v = y(:,2);
% We compute acceleration by using the command diff
a = diff(v);
% Get peaks
accPeaks(i) = max(abs(a));
velPeaks(i) = max(abs(v));
dispPeaks(i) = max(abs(x));
end
figure
subplot(1,3,1)
stem(Ts, accPeaks), grid on
xlabel('Period {T (s)}')
ylabel('Acceleration $(\frac{in}{s^{2}})$', 'interpreter', 'latex', 'fontsize', 18)
title('Spectral Acceleration')
subplot(1,3,2)
stem(Ts, velPeaks), grid on
xlabel('Period {T (s)}')
ylabel('Velocity $(\frac{in}{s})$', 'interpreter', 'latex', 'fontsize', 18)
title('Spectral Velocity')
subplot(1,3,3)
stem(Ts, dispPeaks), grid on
xlabel('Period {T (s)}')
ylabel('Displacement $(in)$', 'interpreter', 'latex', 'fontsize', 18)
title('Spectral Displacement')
%% Report
% In this work an analysis of the dynamics of a structure under the effects of an earthquake (ground acceleration)
% is carried out. Through integration methods and graphical analysis, the results of acceleration, velocity
% and displacement of the structure are analyzed.
% In Figure 1 we can observe the values of the ground acceleration for a time window of 54 seconds.
% We can see that the ground acceleration reaches a maximum peak of 134.6 inches.
% In Figure 2, we can see the dynamic results of the structure. We see that the structure suffers
% a small displacement (maximum 6 inches) thanks to the damping effect that the structure has, which minimizes
% the damage caused by earthquakes.
% In Figure 3 we see the spectral analysis of the structure. This analysis is extremely important since it allows us to detect
% if the structure is prone to greater damage for low or high frequency earthquakes. In this case, we see that
% the structure is prone to damage for low frequencies (high periods), since we see that for longer periods
% the displacement of the structure increases, which means that the oscillation amplitude is greater and
% therefore it can break (taking as an example a structure similar to a skyscraper
```

## Similar Samples

Discover our quality through a variety of programming homework samples. These examples demonstrate our proficiency in handling diverse coding challenges across multiple languages. Check out these samples to see how we can help you achieve excellence in your programming assignments.

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming

Programming