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## Homework Statement

Calculate the horizontal force dF

_{horizontal}of a string .Show that for small oscillations this force is much smaller than the vertical force dF

_{vertical}responsible for the transverse oscillations.

[I apolagize for the way the equations are written]

## Homework Equations

dF

_{vertical}=T

_{0}dy/dx*-T

_{0}dy/dx*

^{1}

*for x+dx *

^{1}for x

T

_{0}(d^2 y/d^2 x)dx=(μ

_{0}dx)d^2 y/dt^2

3. The Attempt at a Solution

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.

dF

_{horizontal}=T

_{0}dx/dy*-T

_{0}dx/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...

T

_{0}(d^2 x/dy^2) dy= (μ

_{0}dx)(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.

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