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+
+//example 6.5
+clc; funcprot(0);
+//exapple 6.5 
+// Initialization of Variable
+rho=1000;
+dc=.15;
+l=7.8;
+g=9.81;
+pi=3.1428;
+atp=105.4*1000;
+vap_pre=10.85*1000;
+sl=.22;
+dp=0.045;
+h=4.6;
+//("x(t)=sl/2*cos(2*pi*N*t)"  "the function of displcement");
+//"since we have to maximize the acceleration double derivate the terms");
+//since double derivation have the term cos(kt) 
+//finding it maxima
+t=linspace(0,5,100);
+k=1;
+function[m,v]= maximacheckerforcosine()
+h=0.00001;
+a=0.00;
+for i=1:400 
+    if (cos(a+h)-cos(a-h))/2*h==0 & cos(i-1)>0 then
+break;
+else 
+    a=0.01+a;
+end 
+break;   
+end
+m=i-1;
+v=cos(i-1);
+endfunction;
+[a, b]= maximacheckerforcosine();
+disp(a,"time t when the acceleration will be maximum(s)");
+//double derivative will result in a square of value of N
+//lets consider its coefficient all will be devoid of N^2 
+k=sl/2*(2*pi)^2//accn max of piston
+kp=k*1/4*pi*dc^2/1*4/pi/dp^2;//accn coeff. ofsuction pipe
+f=1/4*pi*dp^2*l*rho*kp;//force exerted by piston
+p=f/1*4/pi/dp^2;//pressure exerted by piston
+//calculation
+o=atp-h*rho*g-vap_pre;
+//constant term of quadratic eqn
+y=poly([o 0 -p],'N', 'coeff')
+a=roots(y);
+disp(abs(a(1,1)),"Maximum frequency of oscillation if cavitation o be avoided(in Hz)");
+
+
+
+
+
+
+
+