[Torrey, Daniel]

Within the Michelson Interferometer to test the piezo, we disassembled the Piezo assembly. On the back of mirror, there appears to be an etching (see attached photo).

We then added a 1/16 in thick steel spacer with a 1 in OD and 0.25 in ID between the mirror and piezo (see attached photo).

We slightly tweeked the alignment to get good contrast and took open and closed loop transfer functions (see attached photo and data).

We expect the fundamental resonance to be changed by the following: \[f_2 = f_1 \sqrt{\frac{m_1}{m_2}} \] , where f_1 = 8.5 kHz , m_1 = 6.7 g  (the mass of the mirror), and m_2 = 11.6 g (the mass of the mirror plus the spacer).

This predicts f_2 = 6.6 kHz , but we measure f_2 =6 kHz .

Even though there is this 10% discrepancy, this gives us some confidence we are looking at the first longitudinal eigenmode at 8.5 kHz without the spacer.