In a simple pendulum, the displacement of the bob is half of the amplitude. Calculate fraction of PE and KE of the pendulum.

Explanation

Given, `y=(A)/(2)`
We know that `P.E.=(1)/(2)m omega^(2)y^(2)` where `k=omega^(2)=(1)/(2)k((A)/(2))^(2)=(1)/(8)kA^(2)`
`K.E. =(1)/(2)momega^(2)(A^(2)-y^(2))=(1)/(2)k(A^(2)-(A^(2))/(4))=(1)/(2)k((3A^(2))/(4))=(3)/(8)kA^(2)`
But `T.E. = P.E. + K.E. =((1)/(8)+(3)/(8))kA^(2)=(1)/(2)kA^(2)`
Hence `(PE)/(TE)((1)/(8)kA^(2))/((1)/(2)kA^(2))=0.25=(1)/(4)(=25%)`
Similarly, `(KE)/(TE)=((3)/(8)ka^(2))/((1)/(2)kA^(2))=0.75(=75%)`.