A particle is executing SHM. If time is measured from when it is at one end of its path of motion, calculate the ratio of its kinetic energy to the potential energy at t=T/12. Here T is the time period of the motion. Suppose the initial phase is zero.

A particle is executing SHM. If time is measured from when it is at on

1.	A particle is executing SHM. If time is measured from when it is at one end of its path of motion, calculate the ratio of its kinetic energy to the potential energy at t=T/12. Here T is the time period of the motion. Suppose the initial phase is zero.
Answer» Solution :If time is MEASURED from when the particle is at ONE end of the path of motion, then the equation of SHM is `x=Acosomegat`. If `t=T/12`, then `x=A"cos"(2PI)/TT/12=A"cos"pi/6=(Asqrt3)/2=sqrt3/2A` Kinetic energy of the particle at that time, `K=1/2mv^(2)=1/2momega^(2)(A^(2)-x^(2))` = `1/2momega^(2)(A^(2)-(3A^(2))/4)=1/8momega^(2)A^(2)` POTENTIAL energy of the particle at that time, `U=1/2momega^(2)x^(2)=1/2m(omega^(2)(3A^(2))/4)=3/8momega^(2)A^(2)` `therefore""K/U=(1/8momega^(2)A^(2))/(3/8momega^(2)A^(2))=1/3" "thereforeK:U=1:3`.