= Jeffrey Lang
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<Jeffrey Lang> is an <electrical engineer> whose work concerns <electromechanical conversion power balance>, control and small-scale devices. MIT's Research Laboratory of Electronics identifies the same professor as Jeffrey H. Lang and describes research on <electric motors>, <electrical generators> and <microelectromechanical systems>, together with teaching in circuits and electromagnetism.<Jeffrey H. Lang profile by MIT Research Laboratory of Electronics>[Heading; teaching paragraph; electromechanical research paragraph]{ref}
The identified https://www.rle.mit.edu/people/jeffrey-h-lang/[MIT profile] provides an externally hosted https://rledevs4.mit.edu/191402/photo%3Bsmall%3DTrue%3Bversion%3D20141002140122283[portrait of Jeffrey H. Lang].
For an original motor-scale illustration, a shaft delivering <torque> $\tau=2\,\mathrm{mN\,m}$ at <angular velocity> $\omega=1000\,\mathrm{rad\,s^{-1}}$ delivers $P_m=\tau\omega=2\,\mathrm W$. If electrical input is $3\,\mathrm W$ and the operating point is steady, the remaining $1\,\mathrm W$ must be accounted for by losses or another specified output. During acceleration some input can instead increase <rotational kinetic energy>. Reporting only shaft speed would not establish either output <power> or conversion efficiency.
With <Anant Agarwal>, Lang is credited on the MIT course material <State and Memory by Anant Agarwal and Jeffrey Lang>. It explains how a <capacitor>'s state summarizes the part of past input needed to predict its future response.<State and Memory by Anant Agarwal and Jeffrey Lang>[PDF pp.2–6, capacitor state and zero-input/zero-state response]{ref} For a series <RC circuit> with a constant later input $V_f$,
$$
v_C(t)=V_f+\bigl(v_C(0)-V_f\bigr)e^{-t/(RC)}.
$$
Two different earlier input histories that leave the same initial capacitor <electric potential difference> give the same subsequent response under the same future input. For stipulated $RC=1\,\mathrm{ms}$, $v_C(0)=1\,\mathrm V$ and $V_f=3\,\mathrm V$, the value after one <time constant> is $3-2/e\approx2.2642\,\mathrm V$. This original numerical example shows what it means for the state to retain enough of the past without retaining the entire waveform.
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