A one-dimensional spring–mass oscillator has mass m and spring constant k. A graph of speed v against displacement x is a circle in the x–v plane (using the numerical values in the specified units). Which relation is intended?
Options

Question

A one-dimensional spring–mass oscillator has mass m and spring constant k. A graph of speed v against displacement x is a circle in the x–v plane (using the numerical values in the specified units). Which relation is intended?

Options

G1 Physics · Accepted Answer

Step 1: Conservation of oscillator energy gives (1/2)kx² + (1/2)mv² = E. Step 2: Divide by m/2: v² + (k/m)x² = 2E/m. Step 3: A circular locus in numerical x–v coordinates requires equal coefficients of x² and v², so k/m = 1 numerically in the chosen unit scales. Step 4: Therefore k = m numerically. Final answer: k = m (Option B), with the caveat that dimensional units of k and m differ; this is a unit-dependent graph statement.