Physics

Physics

Problem

An 0.40 kg0.40\,\text{kg} block attached to a horizontal spring of force constant 120 N m−1120\,\text{N\,m}^{-1} has a speed of 0.30 m s−10.30\,\text{m\,s}^{-1} when its displacement from equilibrium is 0.020 m0.020\,\text{m}. Find: (i) the amplitude of oscillation, and (ii) the total mechanical energy of the system. a. (i) Amplitude b. (ii) Total mechanical energy
Intuitive explanation

This is a problem about energy conservation in simple harmonic motion. The key insight is that at any point in the oscillation, the total mechanical energy stays constant—it's just split between kinetic energy (from the block's speed) and elastic potential energy (from the spring's stretch). You know the block's position and speed right now, so you can calculate both energy forms at this instant, add them up to get the total, and then use that total to find the amplitude (the point where all energy is potential).

Intuitive explanation

This is a problem about energy conservation in simple harmonic motion. The key insight is that at any point in the oscillation, the total mechanical energy stays constant—it's just split between kinetic energy (from the block's speed) and elastic potential energy (from the spring's stretch). You know the block's position and speed right now, so you can calculate both energy forms at this instant, add them up to get the total, and then use that total to find the amplitude (the point where all energy is potential).

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