A group of physics students are conducting an experiment to test the limits of springs. They have a 400 g block moving on a frictionless surface, which collides with the spring. The velocity of the block and the force exerted on it by the spring during the collision are recorded, as shown in the figure below. What is the duration of the collision - the time the block spends in contact with the spring?

Given the equation: $\(\frac{1}{2}\)(0.20\(\mathrm{~kg}\))\(\left\)(v_{1x}\(\right\))^2+\(\frac{1}{2}\)(3.5\(\mathrm{~N}\)/\(\mathrm{m}\))(0\(\mathrm{~m}\))^2=\(\frac{1}{2}\)(0.20\(\mathrm{~kg}\))(0\(\mathrm{~m}\)/\(\mathrm{s}\))^2+\(\frac{1}{2}\)(3.5\(\mathrm{~N}\)/\(\mathrm{m}\))\(\left\)(\(\Delta\) x_2\(\right\))^2$

Which of the following problem statements is valid for this equation?

A 100 g ball of dough is traveling at 3.0 m/s and strikes another 100 g ball of dough at rest on a frictionless surface. The two balls stick together and then compress a horizontal spring with a spring constant of 3.5 N/m. The other end of the spring is firmly anchored to a fixed post on the surface. Determine the compressed length of the spring.