Physics

Physics

Problem

A 0.50 kg0.50\,\text{kg} block is attached to a spring of force constant 200 N m−1200\,\text{N\,m}^{-1}. Calculate the frequency of its small oscillations. a) 6.4 Hz6.4\,\text{Hz} b) 20 Hz20\,\text{Hz} c) 3.2 Hz3.2\,\text{Hz} d) 1.6 Hz1.6\,\text{Hz}
Intuitive explanation

This is about simple harmonic motion and the relationship between a spring's stiffness and how fast it naturally oscillates. The key insight is that a stiffer spring (larger kk) pulls the block back harder, making it oscillate faster, while a heavier mass oscillates slower because it has more inertia to overcome. You'll use the formula connecting the spring constant and mass to find the natural frequency directly.

Intuitive explanation

This is about simple harmonic motion and the relationship between a spring's stiffness and how fast it naturally oscillates. The key insight is that a stiffer spring (larger kk) pulls the block back harder, making it oscillate faster, while a heavier mass oscillates slower because it has more inertia to overcome. You'll use the formula connecting the spring constant and mass to find the natural frequency directly.

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