Harmonic Oscillation of two point masses

[doublemint]

Hello

I am trying to figure out this following question:
A metronome consists of two point masses m1 and m2 on the ends of a massless rod of length
l. The top mass is m2, which is smaller than m1. The rod pivots about a point at a distance
d from m1. Use Lagrange's method to nd the equation of motion of this metronome, and
nd the condition that d must meet to ensure simple harmonic oscillation. Hint: Use an xy
coordinate system with the origin at the pivot point.
I have solved for the equation of motion but I am unsure what it is meant by finding d so that it satisfies for a SHO. Does it mean d cannot equal 0? or that l-d<d ?
Thanks
DoubleMint

 

[tiny-tim]

Hello DoubleMint!

… Use Lagrange's method to nd the equation of motion of this metronome, and the condition that d must meet to ensure simple harmonic oscillation.

I think it simply means the limit beyond which the motion is exponential rather than restorative.

 

[doublemint]

Thanks tiny-tim!