# Stroboscopy

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Illuminating a moving object with a flashing light can change the apparent speed of the object's motion. This is called the stroboscopic principle, and it is widely used to slow the apparent speed of fast motions (such as the rotation speed of a motor) so as to make them easier for a human to observe.

For this problem, we will consider an object moving in 1 dimension with a periodic motion (with period T), such that x(t) = x(t+T) represents the object's position at time t.

Assume that we observe x(\cdot) using a flashing light that flashes every \Delta seconds. This is equivalent to sampling x(\cdot) to derive a discrete-time signal y[\cdot], given by y[n] = x(n\Delta).

However, our sampling rate is limited so that \Delta > T (that is, we cannot sample faster than once per period of the object's motion).

Find a value of \Delta such that \Delta > T and y[n] = x(nT/10). Explain
your result and your process.

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If not, prove why this is not possible.

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Find all the values of \Delta such that y[n] can be written in the form

where \Omega is in the range 0 \lt \Omega \lt \frac{\pi}{2}.

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