\sect{Galvanometer}
%Baruch's D25
A galvanometer at temperature ${T}$ has a mass $m$, a deflection spring with
an oscillation frequency $\omega_0$ and a damping resistance ${R}$.
The position $x$ of the spring measures the current $I$ via the equation
\[\ddot{x}+\omega_0^2x=-\gamma \dot{x}+A(t)+\alpha I\]
where $A(t)$ is a random force, $\gamma$ is the friction and $\alpha$ is an instrument parameter, converting current into force.
\begin{itemize}
\item [(a)]
What is the lower limit on a current which can be safely
recorded?\\
\item [(b)]
Evaluate the dissipation rate and identify ${R}$ by equating the
dissipation with ${I^{2}R/2}$ where ${I}$ is a current with
frequency $\sim \omega_0$. Rewrite (a) in terms of $R$ (instead of $\alpha$).
\end{itemize}
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