10 (a) Two blocks connected by springs perform small oscillations 21(t) and 22a) around their equilibrium positions. The oscillations are governed by the equations of motion: 221 = 821 + 222 2.2 = 221 322 (i) By assuming solutions of the form 2 = Asin(wt + 95), describe how these equations can be transformed into an eigenvalue problem. (4) (ii) Find the characteristic frequencies and displacement ratio vectors of the system of blocks. (6) (iii) Write down the general solution for the oscillations 21(r) and 22(t). (3) (iv) State, with reasons, whether each of the normal modes found in (ii) are inphase or out-ofphase. (2) (v) Given that the blocks start from their equilibrium position, if the oscillations only consist of the normal mode with highest frequency and at t = 1 the first block is 1 unit away from its equilibrium position, write down the particular solution for the oscillations 21(t) and 22(t). (3)