Discussion
Determine the fundamental period of the signal \(x(t) = \sin 50\pi t\).
Answer: B
For \(x(t) = \sin \omega_0 t\) the fundamental period is \(T = 2\pi / \omega_0\). Here \(\omega_0 = 50\pi\) rad/s.
\[ T = \frac{2\pi}{50\pi} = \frac{1}{25} = 0.04\ \text{s} \]
The frequency is 25 Hz. The value 0.02 s would be the period of a 50 Hz signal, which is what you get if you take \(\omega_0 = 100\pi\), and 0.06 s and 0.08 s have no basis. The answer is 0.04 sec, option B.
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