Question

The system parameters of a freely-vibrating damped SDOF system are as follows: Mass, m= 100 kg Damping Factor, c = 200 kg/s Spring Stiffness, k = 3000 N/m Initial Position, x, = 1 m Initial Velocity, v,= 0 m/s a) Create a MATLAB code and using the specified system parameters compute (using the correct units) the system characteristics: 1) natural (circular) frequency on; 2) cyclic frequency fn; 3) cyclic period p; 4) damped natural (circular) frequency 0g, and 5) damping ratio Š.

Answer 1

giren data; 100 Kg Cニ 2009)s Spoing stitnus k= 3000 Mlm om)s (D) FO Singlc DOF 1 cy clic pea iod P (49 wa=wai-) Cc 21

MATLAB code:

clc;

% input data

m=100;

c=200;

k=3000;

% critical damping coeffcient

cc=2*sqrt(k*m);

% 1) Natural frequency

wn=sqrt(k/m);

% 2) Cyclic frequency

fn=wn/(2*pi);

% 3) cyclic period

Tn=1/fn;

% 4) Damped Natural frequency

wd=wn*sqrt(1-(c/cc)^2);

% 5) damping ratio

zeta=c/cc;

% displaying the values

fprintf('Natural frequency = %d rad/s \n',wn);

fprintf('Cyclic frequency = %d Hz \n',fn);

fprintf('Cyclic Period = %d seconds \n',Tn);

fprintf('Damped Natural frequency = %d rad/sec \n',wd);

fprintf('Damping ratio = %d \n',zeta);