For an oscillating particle, calculate the ratio K/Eₚ at t = T/12, where K is kinetic energy, Eₚ is potential energy and T is the time period.
Physics · Simple Harmonic Motion
JEE Mains Advanced

Question

For an oscillating particle, calculate the ratio K/Eₚ at t = T/12, where K is kinetic energy, Eₚ is potential energy and T is the time period.

G1 Physics · Accepted Answer

Take x=A sinωt. At t=T/12, ωt=2π(T/12)/T=π/6. Therefore U=E sin²(π/6)=E/4 and K=E−U=3E/4. Hence K/U=3.