# Slowing a Mass with a Spring Collision

Coop

## Homework Statement

A 1.5 kg mass slides across a horizontal, frictionless surface at a speed of 2.0 m/s until it collides with and sticks to the free end of a spring with spring constant 50 N/m. The spring's other end is anchored to the wall. How far has the spring compressed when the mass, at least for an instant, is at rest? How much time does it take for the spring to compress to this point?

I don't care about the first part of the question. I am just looking at the second question.

## Homework Equations

$$T (period) = 2\pi\sqrt{\frac{m}{k}}$$

m = mass on the spring
k = spring constant

## The Attempt at a Solution

The answer in my book says to set $$t_{f} = \frac{1}{4}T$$, stating "the motion of the mass until it stops is 1/4 of a cycle of simple harmonic motion." This is why I am confused, isn't the spring only momentarily at rest at the beginning, end and halfway through the period? Isn't the book saying the spring is momentarily at rest one-forth of the way through the period? I don't see why this is true.

Thanks,
Coop