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The ratio of the time periods of small oscillations of the insulated spring and mass system before and after charging the masses is:
At equilibrium keq2/(x2e-x1e)2 = k(x2e-x1e-L) ,where x2eand x1e are respective equilibrium positions . Or, keq2/xe2 = k(xe-L) ,where xe is the separation between the masses at equilibrium. Is it correct ? EOM for mass m1 is m1d2x1/dt2 = kx - keq2 / (x+L)2 EOM for mass m2 is m2d2x2/dt2 = -kx + keq2 / (x+L)2 .
Dear student Charge of small bodies in eqm = (1/4*pie*epselon) q^2/(lo+x0)^2 = kx0 F = -[k(x+x0) - (1/4*pie*epselon) q^2/(lo+x0)^2 ] = -kx , since xa = -2k/m * x F = mew *a mew =m/2 w = sqrt(2k/m) T = 2*pie sqrt(m/2k)T0 = 2*pie sqrt(m/2k)T/T0 = 1
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