Question

2.95. A DVD drive is mounted chassis and is modeled as a single-degree-of-freedom on a spring, mass, and damper. During normal operation, the drive (having a mass of 0.4 kg) is subject to a harmonic force of 1 N at 10 rad/s. Because of material considerations and static deflection, the stiffness is fixed at 500 N/m and the natural damping in the system is 10 kg/s. The DVD player starts and stops during its normal operation provid- ing initial conditions to the module of xo - 0.001 m and vo - 0.5 m/s. The DVD drive must not have an amplitude of vibration larger then 0.008 m even during the transient stage. First, compute the response by numerical simulation to see if the constraint is satisfied. If the constraint is not satisfied, find the smallest value of damping that will keep the deflection less than 0.008 m.
solve using Matlab , write the matlab code please

Answer 1

Single-degree-offreedom spring Mass 0.4kg is subjected to a harmonic force of 1N at 10rad/sec Stiffnes k 500N/m due to material properties ,mass and damper Damping c 10kg/sec Initial condition position 0.001m and velocity 0.5m/sec Xmaxless than or equal to 0.008m = 1sin 10t O m 0.4kg kg Ns k 500 N/m C =10 = 10 sec ground D Alembert's principle, F ma f(t) 1sin 10t = f(t)-cx kx =mx mx+cxkx= f(t) x(t) 0.4x+10x500x sin10t kx Numerical solution using ode45 free body diagram let x x1) f(1) x(2) x = C - x(2) -1250x(1) + 2.5sin 10t 0.4 f(2) x=--

%ode45
clc;clear all;close all
c1=10;
X=0;c=10;
while X~=0.008
t1=[0 5];%time range
C=[0.001;0.5];%initial condition
[t, x] = ode45 (@(t,x) fun_1(t,x,c), t1, C);
X=round(max(x(:,1)),4);
c=c+0.01;
end
if c1==(c-0.01)
fprintf('The constraint is satisfied\nThe value of smallest damping is %1.3fNs/m\n',c1);
else
fprintf('The constraint is not satisfied\nThe value of smallest damping is %1.3fNs/m\n',(c-0.01));
end

The constraint is not satisfied The value of smallest damping is 15.600NS/m