Please solve this problem related to the continuous system of waves

m K L = ( Uit1 - U; ) 2 2 2 (a) In the continuous limit that u. (t) -> u(x,t),mla -> p, Ka - Y, and E du du dx , show that the Lagrangian can be written as L = | I(u, )dx . at ' ax Derive the form of I. (b) Using the least action method S | ldt = 0 (assuming the two ending points of the string are fixed), Derive the equation of motion for u.5. Consider a loaded string with infinite length (see Figure). K m K m K m K W nowm a If the displacement of ith mass is described by ui(t), the Lagrangian is given by