= Solution
The <Nyquist–Shannon sampling theorem> gives a \b[Nyquist rate of $200$ samples per second] for a $100$ Hz upper <frequency>. In practice choose \b[$f_s>200$ Hz], for example $500$ Hz with $\Delta t=2$ ms, and use an <anti-aliasing filter> whose passband retains the required signal below the <Nyquist frequency>. Exactly $200$ Hz leaves no filter transition band and can entirely miss a $100$ Hz sinusoid at an unfortunate phase; it is a limiting rate, not a robust acquisition choice.
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