A particle undergoing simple harmonic motion has an amplitude of 10 ~cm . When the particle is at a displacement of 6 ~cm from the centre, then the ratio of its kinetic energy to potential energy is

Step-by-step solution

Amplitude of particle performing SHM, A=10 ~m Instantaneous displacement of the particle, x=6 ~cm Kinetic energy of the particle, K= 1 2 m ^2 (A^2-x^2 ) Potential energy of particle, aligned U & = 1 2 m ^2 x^2 K U & = 1 2 m ^2 (A^2-x^2 ) 1 2 m ^2 x^2 & = A^2-x^2 x^2 = A^2 x^2 -1 & = ( A x )^2-1= ( 10 6 )^2-1= 25 9 -1 K U & = 16 9 K: U=16: 9 aligned