APPENDIX A 



DYNAMIC CORRECTIONS TO MEASURED FORCES 



The determination of the coefficients in 

 ^j the equations of motion requires that the dis- 



placement of the model, 2{t), be known. Un- 

 fortunately it is not possible to measure the 

 model motion directly but rather the motion 

 above the balance, y{t). Ideally, with an in- 

 z = zge""'' */®' 1 finitely stiff balance, the two would be the 



"yj I ' -7 same. Actually, the balance must be consid- 



y~=^ — '■ ered to be a spring with high spring constant 



■At- 



p. i(ojt-5)l ^) for, being a strain gage balance, it must 



r - ro 6 



'3 



deflect in order to sen«e the forces. 



We wish to know F(t)/z(t) [or M(t)/3(t)] 

 Figure 20 - The Model-Balance ^"t can only measure F (t)/y(t). Using the corn- 



Dynamic System plex representations shown in Figure 20 



<t) 2o y(0 3(0 y^ 3^ L5J 



Thus -^ e~'P is a correction which must be applied to the measured quantity 



or 



Assuming as before that the force on the model is proportional to 2, z, and 2, we can write 

 the force quation 



As + Bz + Cz =k {y-z) 

 or 



Az + Bz + {C + k) z = ky 



substituting z = z^ e'^*"' ■"" ^^ and y = y^ e ""' we obtain 



[( -Aoj^ +C + k) + iBco] z^e'P ^ky^ 



29 



