One end of a thin long uniform string having mass density lambda is fixed to a wall and other end with a block which can move along a vertical rail. The string is horizontal with tension F. The block starts to execute SHM along the rail with amplitude a and angular frequency omega and the energy is transferred to the string. Due to harmonic oscillations of the block a transverse wave is produced which travels along the string with speed v. The energy transferred during one complete oscillation of the block is

 

a)   

(Fa²)/v

 

b)

(²²Fa³)/v²

 

c)

(Fa²)/2v

 

d)

(2Fa²)/v

well,consider a small element of the string..let it be dx..now,when the string slides a transverse force acts on it which is given by F(transverse)= -F dy/dx..

now,energy passing through x per unit time is P= -F dy/dx(dy/dt)..1..now,since y=y(m) sint...differentiating with respect to time and displacement the above expression and substituting in equation 1,we get P= y(m)^2k(omega)Fcos^2(kx - omega t)..during complete oscillation of the block,we have to integrate

P from t to t+T ...substituting y(m)=a and k=omega/v we get P=Fa^2(omega)^2 T/2v..now put T=2 pi/omega...and we get the get the answer as pi a^2 omega F/v..which is option (a)..i am sorry fr the fact that i have not used symbols in solving the problem fr omega and pi..if u have any problem in the solution,plz feel free to ask me..hope u got it..cheers!!