Question

A horizontal spring-mass system oscillates on a frictionless table. If the ratio of the mass to the spring constant is 0.037 kg·m/N, and the maximum speed of the mass was measured to be 4.5 m/s, the maximum extension of the spring will be  cm.

Answer 1

Apply energy conservation to solve the problem:

$$\frac12kx^2=\frac12 mv^2,\\\space\\ x=v\sqrt{\frac mk}=4.5\sqrt{0.037}=0.866\text{ m},$$

or 86.6 cm.