Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

A spring AB with constant k is hooked in the end A to the ceiling. At the end B of the undefomed spring is hooked a mass of weight 100N. At $t=0$ the mass is let free with no initial velocity. Not taking into account the mass of the spring, find the movement of the spring, its period and amplitude.

My suggested solution is as follows. By Hooke's law $F=k(x-x_0)$, where $x_0$ is the position of the end B at the beginning.

They say the force acting on the mass at a position $x$ is $100N-k(x-x_0)N$, and suggest the equation $m\ddot{x}=100g\ddot{x}=100N-k(x-x_0)N$, where g is the acceleration due to gravity.

I think this is wrong and suggest the equation $m\ddot{x}=100g\ddot{x}=k(x-x_0)$

Who is correct?

p.s. I am not interested in the solution of the equation.

share|cite|improve this question
You really should check units in both solution, it's not clear for me what you want to express. In The first solution,you subtract a force from a dimensionless quantity. In your solution I have no dea why you divide 100 by g. Should this be the mass? – Noldig Feb 21 '13 at 11:52
@Noldig Yes, about the first remark, that is what got me stumbled. I believe mass is implicitly assumed equivalent to weight for these problems, since we assume the gravitational force to be constant. For the second one, well mass=weight/gravity, I have clearly stated what g is. Let me change up the question a little bit. – Student Feb 21 '13 at 12:13
The truth is that I never attended the exercises for this class. I attended algebraic geometry instead. I'm having a hard time going through someone else’s notes. – Student Feb 21 '13 at 12:14
mass = weight / gravity is true, but the 100 grams ARE A MASS, so the lefthand side of your eq. has units ma=N, the right hand side kg/a*a = kg has units of kg not N, thats wrong. – Noldig Feb 21 '13 at 12:45
Yes, indeed. I changed it up a little. It is weight now and it's in Newtons – Student Feb 21 '13 at 12:47
up vote 1 down vote accepted

Afer the discussions in the comments this would be my solution:

The l.h.s in the equations of motion is always simply $m\ddot{x}$, the r.h.s contains the sum of all acting forces. So you have gravity and the force of the spring. thats it. $m\ddot{x}=mg-k(x-x_{0})$

share|cite|improve this answer
I see. Thank you. This feels natural. – Student Feb 21 '13 at 12:50

protected by Qmechanic Mar 25 '13 at 16:28

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

Would you like to answer one of these unanswered questions instead?

Not the answer you're looking for? Browse other questions tagged or ask your own question.