Question

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1. Consider a second-order mechanical system as shown below in Figure i. 77n Frictionless support Figure 1 Using Matlab, generate the impulse response for the following conditions: a) m-1 kg, b 2 N-sec/m and four values of k - 3, 10, 100, 1000 N/m. What is the effect of changing the value of k? How does changing the value of k affect your mechanical structure design? What does it not affect? b) m-1 kg, k- 1N/m, and four values of b 0.02, 0.2,0.5, 2.0 sec/m. What is the effect of changing the value of b? How does changing the value of b affect your mechanical structure design? What does it not affect? Investigate the effect of changing only the weight of the mechanical structure to the time response of the system c)

Answer 1

Given tral Forcing funda- impulse es AppAy

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% problem a
m = 1; b = 2;
k =[3 10 100 1000];

% define complex frequency variabel s
s = tf('s');
% plot the impulse response for various values of k
for i = 1:length(k)
X = 1/(m*s^2+b*s+k(i)); % transfer function
% now plot the impulse response
figure(1);
impulse(X);hold on;grid on;
end
legend('k = 3','k = 10','k = 100','k = 1000');

% problem b
m = 1; k = 1;
b =[0.02 0.2 0.5 2];

% define complex frequency variabel s
s = tf('s');
% plot the impulse response for various values of b
for i = 1:length(b)
X = 1/(m*s^2+b(i)*s+k); % transfer function
% now plot the impulse response
figure(2);
impulse(X);hold on;grid on;
end
legend('b = 0.02','b = 0.2','b = 0.5','b = 2.0');

% problem c
m = [1 10 50]; k = 1;
b = 2;

% define complex frequency variabel s
s = tf('s');
% plot the impulse response for various values of m
for i = 1:length(m)
X = 1/(m(i)*s^2+b*s+k); % transfer function
% now plot the impulse response
figure(3);
impulse(X);hold on;grid on;
end
legend('m = 1','m = 10','m = 50');

Impulse Response 0.3 ㅡㅡㅡㅡ k = 10 0.25 k=100 k 1000 0.2 0.15 0.1 0.05 0.05 -0.1 L 0 4 Time (seconds) 2 6

Impulse Response b 0.02 b 0.2 b -0.5 b 2.0 0.8 0.6 0.4 a 0.2 -0.2 0.4 0.6 0.8 20 30 40 Time (seconds) 0 10 50 60 70

Impulse Response 0.4 0.35 0.3 0.25 a 0.2 兰 0.15 40.1 0.05 0 0.05 0.1 m=50 100 150 Time (seconds) 0 50 200 250 300