Question

GENERAL QUESTIONS FOR EVERYONE TO ANSWER INDIVIDUALLY 1) Type the code below in a new m-file in MATLAB and save it as vibration.m 2) Open Matlab and set the Matlab's current directory to your working directory; you may type "Is" in the command window to make sure you see the file vibration.m; 3) Type "edit vibration.m" in the command window to popup the text editor with the file vibration.m open; 4) Modify the file vibration.m to produce results for answering the following questions. You need to hand in four plots with required answers on them. You can save all plots to "pdf files and insert them into a Microsoft word document. Questions: 1) Design an under-damped free mechanical vibration for the system mý+ by ky 0 by choosing the appropriate coefficients m, b, k (different from those already in the code) and specifying initial conditions. Print your resulting plot of y(0), and write the corresponding m, b, k and your choice of initial conditions on your printout. Show why your choice of coefficients makes the system an under-damped free mechanical vibration? 2) Repeat the procedure in I) for a critically-damped free mechanical vibration. 3) Repeat the procedure in 1) for an over-damped free mechanical vibration. 4) For the mass-spring system y+0.01 y+4k 0 with initial position y (0)- 0.01 and initial velocity ý (0) 0.5, design an external force F Fo cos y t such that when the force is applied, the system is at resonance. Print your plotting result and write your choice of Fo and y on the plot. Explain why you choose this y value.

this is the first question

Answer 1

%%% Main File

tspan=[0 4];
%% initial displacement = 0.02m and initial velocity = 0 m/s
y0=[0.02;0];
[t,y]=ode45('vibration',tspan,y0);
plot(t,y(:,1));
grid on
xlabel('time')
ylabel('Displacement')
title('Displacement Vs Time')
legend ('m = 1kg, k = 100 N/M, b = 2, zeta = 0.1, ')
hold on;

%% function file

function yp = vibration(t,y)
m = 1; %% in kg
k = 100; %% in N/m
zeta = 0.1;
wn = sqrt(k/m); %% natural frequency
b = 2*zeta*wn*m
yp = [y(2);(-((b/m)*y(2))-((k/m)*y(1)))];

Displacement Vs Time 0.02 m = 1 kg, k = 100 NM. b-2, zeta = 0.1, 0.015 0.01 0.005 0.005 0.01 0.015 2 2.5 3 1.5 0.5 4 time

-3 x 10 20 Displacement Vs Time m-1kg, k100 N/M, b 20, zeta 1, 15 E 10 -5 2 2.5 3 1.5 0.5 4 time

-3 x 10 20 Displacement Vs Time m- 1kg, k 100 N/M, b 30, zeta- 1.5 15- 10 -5 2 2.5 3 time 1.5 0.5 4

4-

%%Main

%% initial displacement = 0.02m and initial velocity = 0 m/s
y0=[-0.01;0.5];
[t,y]=ode45('forced',tspan,y0);
plot(t,y(:,1));
grid on
xlabel('time')
ylabel('Displacement')
title('Displacement Vs Time')
legend ('f =10, w = 20 ')
hold on;

%% function

function yp = forced(t,y)
m = 1; %% in kg
k = 100; %% in N/m
zeta =0.1;
wn = sqrt(k/m); %% natural frequency
b = 2*zeta*wn*m
w = 2*wn
f = 10
yp = [y(2);(((f/m)*sin(w*t))-((b/m)*y(2))-((k/m)*y(1)))];

Displacement Vs Time 0.15 f=10, w = 20 0.1 , 는 0.05 0.051- -0.1 2 2.5 3 time 1.5 0.5 4