In this note, the classical Doppler shift for some accelerated mechanical systems is considered under a common graphical approach. In one dimension, we study uniform accelerated motion and simple harmonic motion. In two dimensions, uniform circular motion and pendular motion are considered. In each case, an elementary treatment shows that the period (and frequency) measured by an observer at rest depends on the straight paths of two consecutive signals between source and observer, with due consideration of the acceleration.

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