Question

PROBLEM 2 Write a Matlab code* (script) or use Excel to determine the damping coefficient of a spring - mass - damper system with a mass of 165 kg and stiffness of 2400 N/m such that its response will die out (decay) after about 1.5 s, given a zero initial position and an initial velocity of 8 mm/s. 1. Display the numerical value of the damping coefficient. 2. Plot the response of the system. *Turn in your Matlab code with comments Treat this as a quiz. Hence, I will NOT answer specific questions regarding this project. I will answer "general questions.

Answer 1

Natural frequency, k 2400 = 3.81385 = 3.814rad/s 0,= 1165 The equation of motion for the free damped vibration is mx + cx + kx = 0 The general solution of the above equation is x(t)=e=$, (A cos 0,t + Bsin ot) x(0)= 0 0 =(1)( A(1)+B(O)) A=0 x(t)=e**** (Bsin ort) f(t)=-800,$0.4 (B sin ozt)+ 0,30(B cos oat) f(0) = 0.008m/s 0.008 =-60,(1)(B(0))+ 04(1)(B(1)) 0.008 = Boa R 0.008 od x(t) = 0.008640, (sin on,t) 0,= 0, V1-52 The response will die out after 1.5s x(1.5) = 0 0.008 -ěx3.814x1.5 ( sin (0,*1.5)) = 0 sin(0;x1.5)=0 0,*1.5 = sino 0,*1.5 = 0,=radis @,V1 52 2

3.814x vī – 3x3.814 1-2 = 0.075387 $ = 0.961568 c 2mo, 0.961568 = 2x165x3.814 c=1210.249N.s/m x(t) = 0.00$ e$0, (sin 0,1) 0.008 *(= 0.008-290394 sin *(0) – 0.024 3406( sin =)

clc;clear all;close all;
t=0:0.01:4;
x=(0.024/pi).*(exp(-3.665*t)).*(sin(pi*t/3));
plot(t,x)
xlabel('time in sec')
ylabel('x in meter')
grid

xin meter 0.5 1 1.5 2.5 3 3.5 2 time in sec