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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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Simple Harmonic Motion (Horizontal Springs) concept. You can view video lessons to learn Intro to Simple Harmonic Motion (Horizontal Springs). Or if you need more Intro to Simple Harmonic Motion (Horizontal Springs) practice, you can also practice Intro to Simple Harmonic Motion (Horizontal Springs) practice problems.

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