We can describe a nonrelativistic closed string fairly accurately by having the string wrapped around a cylinder of large circumference 27 r on string tension to. we assume that the string out experiencing any friction. let x be a coordinate along the circumference of the cylinder: x + 27t r and let y be a coordinate perpendicular to x, thus running parallel to the axis of the cylinder. as expected, the general solution for transverse motion is given by which it is kept taut by the can move on the surface of the cylinder with- x у(х, 1) — һ+(x — vot) + h-(x + vot), _ where h+(u) and h-(v) are arbitrary functions of single variables u and v with го/ мо- u, v < 0. the string has mass per unit length juo, and vo -oo (a) state the periodicity condition that must be satisfied by y(x, t) on account of the iden- tification that applies to the x coordinate. show that the derivatives h (u) and h' (v) respectively, periodic functions of u and v are, (b) show that one can write h+ (u) — си + f (u), h-(v) bv g(v), where f and g are periodic functions and a and b are constants. give the relation between o and b that follows from (a) (c) calculate the total momentum carried by the string in the y direction. is it conserved?