# Chapter 13 - Exercises and Problems - Page 239: 43

a) $t = \pi \sqrt{\frac{m}{k}}$ b) $x=v\sqrt{\frac{m}{k}}$

#### Work Step by Step

a) We know that the period is given by: $T = 2\pi \sqrt{\frac{m}{k}}$ We know that the time in contact is half of a period, so we obtain: $t = \pi \sqrt{\frac{m}{k}}$ b) We now find the spring's maximum compression. We know that at this point, all of the original kinetic energy will be spring energy. Thus, we find: $\frac{1}{2}mv^2=\frac{1}{2}kx^2\\ mv^2=kx^2\\x = v\sqrt{\frac{m}{k}}$

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