//Estimate of moment of inertia and oscillation frequency of mirror assembly

//(15x15x1) mm mirror weight 0.6 g
//(20x20x1) mm mirror weight 1.1 g
//0.25 inch OD magnet with 0.125 inch ID hole and 0.25 inch long weight 1.2 g
//Small rod (approx 0.125 inch OD and 0.5 inch long) weight 0.7 g

//glass density 2.7
//steel density  7.82
//aluminum density 2.7
//titanium density 4.5
//PTFE density 2.25
//nylon density 1.15

msl=15; //mm mirror side length
mth=1; //mm mirror thickness
pcl=sqrt((msl^2-mth^2)/12); //mm zero-torque centerline for mirror
gth=0.01; //mm glue thickness
rodss=(pcl-(mth/2)-gth)*2; //mm square side length of central rod
rodsl=msl; //mm length of square cross section
rodcd=0.125*25.4; //mm diameter of rod circle cross section
rodcl=0.25*2*25.4+3+3; //mm length of rod circle cross section (both ends)

mm=0.6; //g mirror mass
moi_mirror=mm*(pcl^2+(msl^2)/12); //g*mm^2 moment of inertia mirror (one)
vol_rods=rodss*rodss*rodsl; //mm^3 rod square cross section
rrho=4.5; //g/cm^3 rod material density
mrs=vol_rods*1e-3*rrho; //g mass of rod square cross section
moi_rods=mrs*(rodss^2)/6; //g*mm^2 moment of inertia rod square
vol_rodc=%pi*(rodcd/2)^2*rodcl;
mrc=vol_rodc*1e-3*rrho; //g mass of rod circle (both ends)
moi_rodc=mrc*(rodcd^2)/8; //g*mm^2 moment of inertia rod circle (both ends)
mmg=1.2; //g magnet mass
mgro=(0.25/2)*25.4; //mm magnet OR
mgri=(0.125/2)*25.4; //mm magnet IR
moi_magnet=mmg*0.5*(mgro^2+mgri^2); //g*mm^2 moment of inertia magnet (one)

moi_combined=2*moi_magnet+moi_rodc+moi_rods+2*moi_mirror;
moi_kgm2=moi_combined*1e-9; //kg*m^2
tstf=(0.026*0.5)/(50/180*%pi); //N*m/rad torsional stiffness of reluctance from magnetic simulation for 2 magnets
fres=sqrt(tstf/moi_kgm2)/(2*%pi); //Hz
