Energy in each cycle of transverse wave?

[Sho Kano]

Homework Statement

Homework Equations

The Attempt at a Solution

a. ${ P }_{ avg }=\frac { 1 }{ 2 } \mu v{ \omega }^{ 2 }{ A }^{ 2 }=\frac { 1 }{ 2 } 0.075\frac { 10 }{ 3 } { 0.35 }^{ 2 }{ (10\pi ) }^{ 2 }=15.1W$
b. Not sure how to calculate that... I'm guessing it'd be some integral over 1 period for the kinetic energy involved in the up down movement of the string plus some integral for the potential energy involved with the string's tension over 1 wavelength. How do I construct these integrals?

 

[Sho Kano]

Never mind! $\omega =10\pi =\frac { 2\pi }{ T } \\ T=\frac { 1 }{ 5 } s\\ PT=\frac { J }{ s } s=J=15\frac { 1 }{ 5 } =3J$

 

[Sho Kano]

I know I can do this using an integral. But how?