An ant with mass `m` is standing peacefully on top of a horizontal, stretched rope. The rope has mass per unit length `mu` and is under tension `F`. Without warning, a student starts a sinusoidal transverse wave of wavelength `lambda` propagating along the rope. the motion of the rope is in a verticle plane. what minimum wave amplitude (in mm) will make the ant feel weightless momentarily? Assume that `m` is so small that the presence of the ant has no effect on the propagation of the wave.
[Given: `lambda=0.5 m,mu=0.1 kg//m,F=3.125 N,take g=pi^(2)`]

Explanation

`a_(max)=omega^(2)A=g`
`omega=(2piv)/(lambda)`, `v=sqrt((F)/(mu))`
`A_(min)=(glambda^(2)mu)/(4pi^(2)F)=(lambda^(2)mu)/(4F)=2xx10^(-3)m=2 mm`
force towards equilibrium position `(kx' sin theta)=dk(tantheta-(3 sintheta)/(4))` due to one spring and
net`=2dk(tantheta-(3sintheta)/(4))` for small `theta`, force
`=2dk[theta-(3theta)/(4)]=k(dtheta)/(2))`
`dtheta=` displacement from mean position
`impliesF-(kx)/(2)impliesT_(B)=2pisqrt((2m)/(k))`
`(T_(B))/(T_(A))=2pisqrt((m)/(2K))//2pisqrt((m)/(2K))`
`rArr(T_(B))/(T_(A))=2`