A 52.5 kg mass attached to a spring oscillates with an amplitude of 1.95 m. The total mechanical energy of the system is 395 J. Find the position of the mass when its speed is 2.00 m/s.

I got my answer to be 1.43m, but the online grader said it's wrong. HELP!!

Question

A 52.5 kg mass attached to a spring oscillates with an amplitude of 1.95 m. The total mechanical energy of the system is 395 J. Find the position of the mass when its speed is 2.00 m/s.

I got my answer to be 1.43m, but the online grader said it's wrong. HELP!!

underhill · Answer

$$395 J = 1/2(k)(1.95m)^2$$
Find the spring constant k from the equation above.

Then you can use the following equation to find the position of the mass at a certain speed:$$Total ME = PE + KE$$
$$395 J = 1/2(k)(x^2) + 1/2(52.5kg)(v^2)$$
I get a different answer than the one you posted.

underhill · Answer

By the way, the potential energy of a spring is $$1/2(k)(x^2)$$NOT$$1/2(k)(x)$$as was posted in answer to your previous question.