A uniform bar of length "l" and mass "m" is supported at its ends by two springs. One spring has twice the stiffness of the other. From the equilibrium position the centre of the bar is pulled down a short distance and then released. How do you calculate the displacement "s" of the centre of gravity with respect to time? This is a self inflicted question after looking at the vibrations of weights on springs. I am not a student (63 years old) just interested in physics. I am assuming that the springs at either end of the bar will oscillate with simple harmonic motion of different frequencies (one twice the other) but how do they combine at the centre.