The ratio of kinetic energy to the potential energy of a particle executing SHM at a distance equal to half its amplitude, the distance being measured from its equilibrium position is

Step-by-step solution

Kinetic energy of particle executing SHM is ( K E= 1 2 m ² (A²-y² ) ) Hey ( y= A 2 ) ( K E= 1 2 m ² (A²- A² 4 )= 1 2 m ² 3 A² 4 ) Potential energy of particle executing SHM is ( P E= 1 2 m ² y²= 1 2 m ² A² 4 ) Then ratio of kinetic energy to potential energy is ( K E P E = ( 1 2 ) m ² ( 3 4 ) A² ( 1 2 ) m ² A² 4 = 3 1 ) Therefore, the ratio is ( 3: 1 ).