Graph below shows kinetic energy of three simple harmonic oscillators consisting of different masses, m_1, m_2,and m₃), and different springs with spring constants, k_1, k_2,and k₃),as a function of mass' displacement from equilibrium. If all three oscillators have the same period, what can you say about the spring constants and masses of the oscillators? A) k???₁ is the smallest and k₃ is the largest. B) The ratio of _?k/m is the same for each spring. C) k₂_?_?is smaller than k₃ and m₂ is larger than m₁. D) Neither of the statements A, B, and C is correct. E) All statements A, B, and C are correct.

Question

Quizplus · Accepted Answer

From the graph, we see that the kinetic energy curves of all three oscillators have the same shape with different amplitudes, which indicates that they have the same period. 
Statement A is correct because the period of a simple harmonic oscillator depends only on the spring constant and mass, and a smaller spring constant requires a larger mass to maintain the same period. 
Statement B is correct because the ratio of k/m for each oscillator determines the angular frequency (ω) and period (T), and since they have the same period, they must have the same ω and k/m ratio. 
Statement C is correct because from the graph, we see that the oscillator with the smallest mass and spring constant has the largest amplitude, which corresponds to a larger period, so the oscillator with a larger mass and spring constant should have a smaller period.

Graph Below Shows Kinetic Energy of Three Simple Harmonic Oscillators