Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

My textbook gives the following for x as a function of time for a lightly damped harmonic oscillator: $$ x = Ae^{- \gamma t} \cos (\omega \, t)$$ for $\gamma = \dfrac b {2m}$.

It says this implies the amplitude follows the relationship: $$x_{max} = Ae^{-\gamma t}$$

I am not understanding where this second equation comes from. Why does the cosine term disappear if $\omega$ is a constant?

share|improve this question

1 Answer 1

up vote 0 down vote accepted

$\cos (\omega t)$ behaves like any other cosine term. $\cos (c)$ where $c$ is any constant is itself a constant. Since cosine oscillates between $[ -1 , 1]$ then when cosine is at it's maximum value it can be replaced with $1$.

Therefore: $$x_{max} = max(Ae^{- \gamma t} \cos (\omega t)) = Ae^{- \gamma t} \cdot max(\cos (\omega \, t)) = Ae^{- \gamma t} \cdot 1 = Ae^{- \gamma t}$$

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.