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Which of the following functions of time...

Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic , and (c) non-periodic motion ? Give period for each case of periodic motion `, omega` is any positive constant). ltbr. (a) `sinomegat-cosomegat)` (b) `sin^(3)omegat` (c) `3cos((pi)/(4)-2omegat)`
(d) `cosomegat+cos3omegat+cos5omegat)` (e) ` exp(-omega^(2)t^(2))` (f) `1+omegat+omega^(2)t^(2)`

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To solve the question, we will analyze each function of time given in the problem to determine whether it represents simple harmonic motion (SHM), periodic but not SHM, or non-periodic motion. We will also find the period for each case of periodic motion. ### Step-by-Step Solution: 1. **Function (a): \( \sin(\omega t) - \cos(\omega t) \)** - This function can be rewritten using the identity for the sum of sine and cosine: \[ \sin(\omega t) - \cos(\omega t) = \sqrt{2} \sin\left(\omega t - \frac{\pi}{4}\right) ...
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