1. The problem statement, all variables and given/known data Calculate the horizontal force dFhorizontal of a string .Show that for small oscillations this force is much smaller than the vertical force dFvertical responsible for the transverse oscillations. [I apolagize for the way the equations are written] 2. Relevant equations dFvertical=T0dy/dx*-T0dy/dx*1 *for x+dx *1 for x T0(d^2 y/d^2 x)dx=(μ0dx)d^2 y/dt^2 3. The attempt at a solution 1.substituting y+dy and y for x+dx and x; substituting dx/dy for dy/dx for horizontal oscillation. dFhorizontal=T0dx/dy*-T0dx/dy*1 *for y+dy *1 for y 2.exchanging d^2 y/ dx^2 with d^2 x/dy^2 and dx with dy... T0 (d^2 x/dy^2) dy= (μ0dx)(d^2 x/dt^2) This is as far as I get. I dont know how to show that the horizontal force is smaller than the vertical force for small oscillations. Thanks for any clarifications and corrections.