1.

When the displacement of a particle executing SHM is one-fourth of its amplitude, what fraction of the total energy is the kinetic energy?A. `(16)/(15)`B. `(15)/(16)`C. `(3)/(4)`D. `(4)/(3)`

Answer» Correct Answer - B
In SHM,
Kinetic energy of the particle, `K=(1)/(2)momega^(2)(A^(2)-x^(2))`
where m is the mass of particle, `omega` is its angular frequency, A is the amplitude of oscillation and x is its displacement.
At `x=(A)/(4),K=(1)/(2)momega^(2)[A^(2)-((A)/(4))^(2)]=(1)/(2)((15)/(16)momega^(2)A^(@))`
Energy of the particle, `E=(1)/(2)momega^(2)A^(2)`
`therefore=(K)/(E)=((1)/(2)((15)/(16)momega^(2)A^(2)))/((1)/(2)momega^(2)A^(2))=(15)/(16)`


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