Period:

$\overline{){\mathbf{T}}{\mathbf{=}}{\mathbf{2}}{\mathbf{\pi}}\sqrt{\frac{\mathbf{m}}{\mathbf{k}}}}$

**a)**

If the mass is doubled, T is given as:

$\begin{array}{rcl}\mathbf{T}& \mathbf{=}& \mathbf{2}\mathbf{\pi}\sqrt{\frac{\mathbf{2}\mathbf{m}}{\mathbf{k}}}\\ & \mathbf{=}& \mathbf{\left(}\sqrt{\mathbf{2}}\mathbf{\right)}\mathbf{T}\mathbf{}\mathbf{=}\mathbf{\left(}\sqrt{\mathbf{2}}\mathbf{\right)}\mathbf{(}\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{)}\end{array}$

A block oscillating on a spring has period T = 2.0s

a) What is the period if the block's mass is doubled? Explain.

b) What is the period if the value of the spring constant is quadrupled?

c) What is the period if the oscillation amplitude is doubled while *m* and *k* are unchanged?

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