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A toy of mass 0.50 kg hangs from a spring and stretches it by 8.0 cm…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A toy of mass $0.50\ \text{kg}$ hangs from a spring and stretches it by $8.0\ \text{cm}$ . Find the spring constant and the period of the toy's small up and down oscillations. Take $g = 9.8\ \text{m/s}^2$ .

Need a reminder? The key ideaShow

A hanging spring rests at a stretch $d$ with $kd = mg$ , and $T = 2\pi\sqrt{m/k} = 2\pi\sqrt{d/g}$ . In parallel $k = k_1 + k_2$ ; in series $\dfrac{1}{k} = \dfrac{1}{k_1} + \dfrac{1}{k_2}$ . A piece of a spring has a larger $k$ : $k \times$ length stays the same.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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