. . . . . . . . 's m '11] 1. (34 paints) A twodimensmnal non-isotropic oscrllator conmsts of a small mead t:- a} . . - - 1 en.1ca four springs, as shown 1n the gure. The two springs along the I arms are with spring constant 4.51;, and the two springs along the y-axis are identical with spring constant 8k, where k is a positive constant. (a) (10 points) Express the angular frequencies for the motion in the x-direction and for the motion in the y-direction in terms of to, where w = t/k/m. Hint: When a mass m is attached to two springs of spring constants k; and k2, stretched along the same straight line, the angular frequency for the motion is \\/(k1+ k2)/m. (b) 8 points) For small oscillations, write down the most general solutions :r(t) and y(t). You may use any arbitrary constants you need. Simply state which ones are your arbitrary constants. (c) (16 points) Suppose, at t = 0, the mass was held at $0 = A, yo = 0 and was given an initial speed of exp = 0, 'pr = SwA. (Assume A is very small.) Determine all the arbitrary constant you introduced in part (b)