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]
*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.
*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.