Physics

Physics

Problem

Two identical masses are attached to separate horizontal springs. Spring X has constant kk, and the mass oscillates with amplitude 0.60 m0.60\,\text{m}. Spring Y has constant 2k2k, and the mass oscillates with amplitude 0.30 m0.30\,\text{m}. Calculate the ratio EY/EXE_Y/E_X of their total mechanical energies.
Intuitive explanation

The key is recognizing that total mechanical energy in a spring system depends on both the spring constant and amplitude through the formula E=12kA2E = \frac{1}{2}kA^2. Since both masses are identical and oscillating horizontally, you don't need to worry about gravity or other complications—just compare how the stiffer spring and smaller amplitude trade off to determine which system stores more energy overall.

Intuitive explanation

The key is recognizing that total mechanical energy in a spring system depends on both the spring constant and amplitude through the formula E=12kA2E = \frac{1}{2}kA^2. Since both masses are identical and oscillating horizontally, you don't need to worry about gravity or other complications—just compare how the stiffer spring and smaller amplitude trade off to determine which system stores more energy overall.

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