(a) Without any mathematical detail, use your physical intuition to deduce the normal frequency for symmetric-stretch vibrations. (b) Show that the equations of motion of the three masses are: d?x, + wžx, – wix2 = 0, dt2 d?x2 wžx1 + 2wžx2 – wžx3 = 0 dt² d²x; and - wix2 + w}x3 = 0, where wi = and wž = k/M dt² (c) Assume x1 = A coswt, x2 = B cos wt, and x3 = C coswt. Show that the normal frequencies of the system are vk/m and vk(2m + M)/Mm

(a) Without any mathematical detail, use your physical intuition to deduce the normal frequency for symmetric-stretch vibrations. (b) Show that the equations of motion of the three masses are: d?x, + wžx, – wix2 = 0, dt2 d?x2 wžx1 + 2wžx2 – wžx3 = 0 dt² d²x; and - wix2 + w}x3 = 0, where wi = and wž = k/M dt² (c) Assume x1 = A coswt, x2 = B cos wt, and x3 = C coswt. Show that the normal frequencies of the system are vk/m and vk(2m + M)/Mm