**Part (a)**

Maximum speed is obtained as:

$\begin{array}{rcl}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{\mathbf{v}}^{\mathbf{2}}& \mathbf{=}& \frac{\mathbf{1}}{\mathbf{2}}\mathbf{k}{\mathbf{A}}^{\mathbf{2}}\\ {\mathbf{v}}^{\mathbf{2}}& \mathbf{=}& \frac{\mathbf{k}{\mathbf{A}}^{\mathbf{2}}}{\mathbf{m}}\\ \mathbf{v}& \mathbf{=}& \sqrt{\frac{\mathbf{k}{\mathbf{A}}^{\mathbf{2}}}{\mathbf{m}}}\end{array}$

A mass is oscillating with amplitude A at the end of a vertical spring of spring constant k.

Part (a) The mass is increased by a factor of four, keeping A and k constant. What is true about the maximum speed?

Part (b) The amplitude is doubled, keeping mass and k constant. What is true about the period?

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