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Simple Harmonic Motion Question - Physics

A certain mathematical model is often used to describe the oscillations of atoms in a diatomic model. In it, two unequal masses, m1 and m2 are connected by an ideal spring of natural length, L and spring constant, k. The masses are placed on a horizontal frictionless plane, initially with separation, L. They are then drawn apart slightly so that m1, is a distance a1, and m2 a distance a2, from their original positions. When released, each mass oscillates about its original position with simple harmonic motion of period T, but different amplitudes a1 and a2. The system as a whole does not move along the plane.

Find the amplitudes of a1/a2

I don't know where to start. Thanks
(Image Below)
diamotimc .jpg
(edited 1 year ago)
Is it this question
https://isaacphysics.org/questions/diatomic_molecule_num?stage=all
as youve missed off the bit about the given mass ratio. The hint (5) is to consider the total momentum and relate that to the angular speed of the masses.
(edited 1 year ago)
Reply 2
Original post by mqb2766
Is it this question
https://isaacphysics.org/questions/diatomic_molecule_num?stage=all
as youve missed off the bit about the given mass ratio. The hint (5) is to consider the total momentum and relate that to the angular speed of the masses.


Yes, that is the question.
I can appreciate the equations that go into it being a=-w^2•A, F=ma, w=(2pi)/T, but to find a1 and a2 I don’t understand.
In the hints they say total momentum must be zero at all time, even when the displacements are zero and the velocities are at their maximum value. The velocities depend on initial amplitudes. That allows you to write down the amplitude ratio.

The solution is just a couple of lines, the question is longer than the solution.

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