Physics

Physics

Problem

An object executes simple harmonic motion with amplitude 3.0 cm3.0\,\text{cm} and period 0.80 s0.80\,\text{s}. What is the object’s maximum acceleration? a) 3.7 m/s23.7\,\text{m}/\text{s}^2 b) 7.4 m/s27.4\,\text{m}/\text{s}^2 c) 1.9 m/s21.9\,\text{m}/\text{s}^2 d) 0.24 m/s20.24\,\text{m}/\text{s}^2
Intuitive explanation

Simple harmonic motion always has its maximum acceleration at the extreme points—where the restoring force is strongest and displacement is largest. The key is connecting the period to angular frequency ω=2π/T\omega = 2\pi/T, then using amax⁡=ω2Aa_{\max} = \omega^2 A to find how quickly the velocity must change as the object reverses direction.

Intuitive explanation

Simple harmonic motion always has its maximum acceleration at the extreme points—where the restoring force is strongest and displacement is largest. The key is connecting the period to angular frequency ω=2π/T\omega = 2\pi/T, then using amax⁡=ω2Aa_{\max} = \omega^2 A to find how quickly the velocity must change as the object reverses direction.

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