Physics

$F=−kx$

Then fundamentally this equation represents simple harmonic motion.

Example : Explain whether Functions 1. $sinωt+cosωt$ and 2. $e_{−ωt}$ are periodic or not?

1. we can write $sinωt+cosωt$ as $2 sin(ωt+4π )$

= $2 sin(ωt+4π +2π)$

= $2 sin[ω(t+ω2π )+4π ]$

The periodic time of function is $ω2π $

So it is periodic motion.

2. The function $e_{−ωt}$ decreases monotonically with increasing time and tends to zero as t approaches infinity and thus never repeats its value.

Hence it is non periodic motion.

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