A string of length `50 cm` is vibrating with a fundamental frequency of `400 Hz` in horizontal position. In the fundamental mode the maximum displacement at the middle is `2 cm` from equilibrium position and the tension in the string is `10 N`. Determine the maximum value of the vertical component of force on the end supporting.

Explanation

`F_(y) = T sin theta = t sin theta`
`= T(dely)/(delx)`
`y = A sin (omegaT - kx)`
`= 0.02 sin(omegat - (2pi)/(0.80 xx 2)x)`
`(dely)/(delx) = -0.02 xx (pi)/(0.80) cos (omegat - (pi)/(0.80) x)`
At `x = 0`
`(dely)/(delx) = -(2)/(80) pi cos omegat`
`[(dely)/(delx)]_(max) = (pi)/(40)`
`F_(y) = [T(dely)/(delx)] = (10pi)/(40) = (pi)/(4) Ns`