A taut string has one end, at x = 0, fixed on the axis while the other end, at x = L, is forced to undergo periodic vertical motion described by g(t) = A sin wt, t20 (A is a constant). If the string is initially at rest on the x axis, show using seperation of variables technique that its subsequent displacement is 00 u(x,t) = 2CA (-1)" nnct ndix n212c2 w2L2 (wl sin - nic sin wt) sin L L n=1 What is the critical forcing frequency w for resonance to occur? A taut string has one end, at x = 0, fixed on the axis while the other end, at x = L, is forced to undergo periodic vertical motion described by g(t) = A sin wt, t20 (A is a constant). If the string is initially at rest on the x axis, show using seperation of variables technique that its subsequent displacement is 00 u(x,t) = 2CA (-1)" nnct ndix n212c2 w2L2 (wl sin - nic sin wt) sin L L n=1 What is the critical forcing frequency w for resonance to occur