#### Algebraic derivation

The above equivalent forms are readily verified by deriving the transfer function from the striking-force input to the output force signal

Referring to Fig.6.15, denote the input hammer-strike transform by and the output signal transform by . Also denote the loop-filter transfer function by . By inspection of the figure, we can write

Solving for the input-output transfer function yields

The final factored form above corresponds to the final equivalent form shown in Fig.6.17.

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