Two equal masses are connected by means of a spring and two other identical springs fixed to rigid supports on either side (Fig. 1.3), permit the masses to jointly undergo simple harmonic motion along a straight line, so that the system corresponds to two coupled oscillations. Assume that m1 = m2 = m and the stiffness constant is k for both the oscillators.
(a) Form the differential equations for both the oscillators and solve the coupled equations and obtain the frequencies of oscillations.
(b) Discuss the modes of oscillation and sketch the modes.