## Solution

According to the Shannon Sampling Theorem, you can maintain the frequency content of the signal by sampling at the Nyquist rate; i.e. using a sampling frequency at least twice the maximum frequency component in the sampled signal. Maintaining the frequency content does not mean maintaining the signal shape.

If you want to receive a proper signal shape, as a rule of thumb, you should sample at 10 times the signal frequency; i.e. if the sinusoidal is at 50Hz, you should sample at 500Hz, which means a sampling period of 2ms.

This

link demonstrates different cases on sampling, showing clearly the difference in shape when sampling at 10 times the frequency of the input signal.