Consider a spring mass simple harmonic oscillator in one dimension. The mass of the particle is m kg and the spring constant is k N/m. At a given instant the extension of the spring is x meter and the speed of the particle is v m/s. On the x-v plane, if the graph of v as a function of x is a circle, then the correct option is

Consider a spring mass simple harmonic oscillator in one dimension. The mass of the particle is m kg and the spring constant is k N/m. At a given instant the extension of the spring is x meter and the speed of the particle is v m/s. On the x-v plane, if the graph of v as a function of x is a circle, then the correct option is

v² = ω²(A² - x²)

v² =

k m

(A² - x²)

ω² =

km

v² =

kA² m

-

kx² m

kx² m

+ v² =

kA² m

— (i)

Equation of a circle:

x² + y² = R² — (ii)

∴ On comparing both (i) & (ii):

k m

= 1 ,  

k = m