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+clc

+clear

+mprintf('Mechanical vibrations by G.K.Grover\n Example 5.7.2\n')

+//given data

+W1=220*2*%pi/60//vibrating frequency at 220 RPM (in rad/sec)

+W2=W1//frequency to which the spring mass system is tuned to.

+M2=1//mass in spring mass system in kgs

+N1=188//first resonant freq of spring mass system in cpm

+N2=258//second resonant freq of spring mass system in cpm

+//u=ratio of absorber mass to main mass i.e M2/M1

+//calculations

+K2=M2*W2^2

+Wn1=N1*2*%pi/60//first resonant freq of spring mass system in rad/sec

+Wn2=N2*2*%pi/60//second resonant freq of spring mass system in rad/sec

+//case 1

+W=Wn1

+x1=(W/W2)

+u1=[x1^2-1]^2/x1^2//from Eqn 5.7.9,Sec 5.7.1.

+//case 2

+W=Wn2

+x2=(W/W2)

+u2=[x2^2-1]^2/x2^2//from Eqn 5.7.9,Sec 5.7.1.

+//therefore

+u=(u1+u2)/2//which is equal to M2/M1

+M1=M2/u// mass of main system in kgs

+K1=K2/u//stiffness of main system in N/m

+//now

+Wn21=150*2*%pi/60//new first resonant frequency in rad/sec

+Wn22=310*2*%pi/60//new second resonant frequency in rad/sec

+W=Wn21

+x1=(W/W2)

+u1=[x1^2-1]^2/x1^2//from Eqn 5.7.9,Sec 5.7.1.

+//case 2

+W=Wn22

+x2=(W/W2)

+u2=[x2^2-1]^2/x2^2//from Eqn 5.7.9,Sec 5.7.1.

+//choosing the higher value

+if u1>u2 then

+    u=u1

+else

+    u=u2

+end

+M3=M1*u// mass of main system in kgs

+K3=K1*u//stiffness of main system in N/m

+//output

+mprintf(' The mass of main system required is %4.4f kgs\n stiffness of main system reqired is %5.5f N/m\n If the resonant frequencies lie outside the range of 150 to 310 rpm then\n mass of main system is %4.4f kgs\n stiffness of main system is %5.5f N/m',M1,K1,M3,K3)