At what displacement (i) the P.E. of a simple harmonic oscillator is maximum and minum (ii) the K.E. is maximum and minmum?

Explanation

The P.E. of a particle executing SHM is given by, `U=(1)/(2)momega^(2)y^(2)`
U is maximum when `y=a=` amplitude of vibration i.e., the particle is passing from the extremen position and is minimum when `y=0, ` i.e., the particle is passing from the mean position:
The K.E. of a particle executing SHM is given by `K=(1)/(2)momega^(2)(a^(2)-y^(2))`
K is maximum when `y=0`, i.e., the particle is passing from the mean position and K is minumum when `y=a` i.e., the particle is passing from the extremen position.