Find the period of small oscillations in a vertical plane performed by a ball of mass `m=40g` fixed at the middle of a horizontallly stretched string `l=1.0m` in length. The tension of the string is assumed to be constant and equal to `F=10N`.

Explanation

Let us locate and depict the forces ating on the ball at the position when it is at a distance `x` down form the undeformed position of the string.
At this position, the unbalanced downward force on the ball
`=mg-2 F sin theta`
By Newton's lay `m ddot(x)=mg -2F sin theta`
`=mg-2 Ftheta`( when `theta` is small)
`= mg - 2 F (x)/(l//2)= mg - (4F)/(l ) x `
Thus `ddot(x)=g-(4F)/(ml)x=-(4F)/(ml)(x-(mgl)/(4F))`
putting `x^(')=x-(mgl)/(T),` we get
`ddot(x)^(')=-(4T)/(mgl)x^(')`
Thus `T=pisqrt((ml)/(F))=0.2s`.