Kinematics: Spring Homework Solution

[nahanksh]

Homework Statement

http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam2/sp08/fig11.gif
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

Homework Equations

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?

 

[Doc Al]

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?

 

[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

 

[nahanksh]

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?

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 ...?

 

[Doc Al]

From this point, how do i decide whether it's C or D ...?

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.