Q. 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⁻¹. At a given instant, the extension of the spring is x meter and the speed of the particle is v m s⁻¹. On the x − v plane, if the graph of v as a function of x is a circle, then the correct option is:
A) $k=\sqrt m$
B) $k=1/m$
C) $k=m$
D) $k=m^2$
Explanation
[Solution from source] Energy conservation gives $\frac12kx^2+\frac12mv^2=E$, an ellipse in the x–v plane. It is a circle only when the semi-axes are equal, i.e. k = m numerically (ω = 1 rad s⁻¹). Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.