# Kinematics - Spring

1. Jan 10, 2010

### nahanksh

1. The problem statement, all variables and given/known data
http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam2/sp08/fig11.gif [Broken]
A mass m is attached to a spring with spring constant k, the other end of which is attached to the ceiling. It is pulled and allowed to oscillate up and down. Using dimensional analysis, determine which of the following is a valid expression for the time t it takes to complete each oscillation.
(a) t = 2πkm
(b) t = 2π sqrt(m-k)
(c) t = 2π sqrt(m/k)
(d) t = 2π sqrt(k3/m)
(e) t = 2π + m/k2

2. Relevant equations

3. The attempt at a solution

I tried to solve this problem using 'energy conservation' theorem..
But from there, i couldn't find the factor of the 'time' and when seeing the options given,
I don't even know why "2*pi" is coming into the picture when dealing with spring...

Please could someone help me out here?

Last edited by a moderator: May 4, 2017
2. Jan 10, 2010

### Staff: Mentor

All you have to do is eliminate the equations that can't possibly be valid. Check the units (or dimensions) of each term on the right hand side. Do they match the units of the left hand side?

3. Jan 10, 2010

### payumooli

from free body diagram you can arrive to this eqn
mx'' + kx = 0
this is a simple harmonic motion
x'' + (k/m)x = 0
ω = sqrt(k/m)
ω = 2*pi*f
f = 1/t

4. Jan 10, 2010

### nahanksh

Oh, that was the point of the question.

So, I have eliminated A,B and C.
From this point, how do i decide whether it's C or D ...?

5. Jan 10, 2010

### Staff: Mentor

By checking the units as I described above. What are the units on the right hand side of each? (Only one of them has the correct units.)

You should be doing the same analysis for each term on the right hand side.