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Question 1.
What do we need to change in order to double the total energy of a mass oscillating at the end of a spring?
(a) increase the angular frequency by $\sqrt{2}$.
(b) increase the amplitude by by $\sqrt{2}$.
(c) increase the amplitude by $2$.
(d) increase the angular frequency by $2$.
(e) increase the amplitude by $4$ and decrease the angular frequency by $\frac{1}{\sqrt{2}}$.

The correct answer is given as B, but from my calculations, option A is correct. What am I doing wrong? Also, I can't find a relationship between amplitude and energy.

$$\begin{align} KE_\text{max} &= \frac{1}{2} mv_\text{max}^2 \\ &= \frac{1}{2}m(rω)^2 \\ &= \frac{1}{2}mr^2ω^2 \\ KE'_\text{max} &= \frac{1}{2}mr^2(\sqrt{2}ω)^2 \\ &= mr^2ω^2 \\ &= 2KE_\text{max} \end{align}$$

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Hi user23248, and welcome to Physics Stack Exchange! Generally we discourage questions that just ask for someone to check your work. Once you have identified the specific concept that you're not sure about, that's the point at which it's appropriate to ask a question here. In particular, what do you think you're doing wrong? Also, do you have reason to think there is no relationship between amplitude and energy? Edit some more details on those points into the question, and I'll be happy to reopen it. –  David Z Apr 17 '13 at 0:32
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closed as too localized by David Z Apr 17 '13 at 0:31

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