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- Homework Statement
- Two masses m1 and m2 on the x axis are connected by a spring. The spring has stiffness s, length l and extension x. m2 is at position x2 and m1 at position x1. The equations of the motion are

m1d^2x1/dt^2 = sx and m2d^2x2/dt^2 = -sx

Combine these to show that the angular frequency is w = sqrt(s/M)

Where M = m1m2/ m1 + m2 (the reduced mass)

- Relevant Equations
- m1d^2x1/dt^2 = sx and m2d^2x2/dt^2 = -sx

w = sqrt(s/M)

M = m1m2/ m1 + m2

tried writing the x position as

x = Acos(wt) (ignoring the phase)

so that d

Substituting that into the individual motion equations would get the required result for the individual masses, but I am not sure how to combine the equations to get the reduced mass

x = Acos(wt) (ignoring the phase)

so that d

^{2}x / dt^{2}= -w^{2}xSubstituting that into the individual motion equations would get the required result for the individual masses, but I am not sure how to combine the equations to get the reduced mass