The Art of Practical and Precise Strain Based ... - Webprofile.info

Applications Note 1-9:Where:dMA = M q0 () t = F2d t2(EQ 1-22)Substituting (1-22) for MA in (1-21) and solving for q i (t) yields:2d dq i () t = M q0 () t + R q0 () t + Kq2d t dt0 () t(EQ 1-23)Converting from the time domain into the frequency domain using the relationshipq i (t) = e jwt as representative of a sinusoidal input, and knowingthat the output will equal:q 0 () t = H( w)q i () t(EQ 1-24)(where H(w) is the system transfer function)Then, the output must be of the form:q 0 () t = H( w)e jwt(EQ 1-25)H(w) also represents phase as well as magnitude of response. Havingestablished this equality, differentiation of equation (1-25) yields the furtherequalities:d q0 () t = H( w)jwe jwtdt(EQ 1-26)and2d q0 () t = ÐH( w)w 2 e jwtdt 2(EQ 1-27)Substitution of equations (1-24), (1-25), (1-26), and (1-27) into equation(1-23) and solving for H(w) yields:The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999 CHAPTER 1-53