Mass-Spring System
BINAS 35B1Tsokos Ch. 9.2
Overview
A mass m on a spring with spring constant k oscillates with period T = 2π√(m/k). Key insight: period depends only on m and k — NOT on amplitude. Doubling A does not change T. To increase period: increase mass or decrease spring stiffness. The spring constant k has units N/m.
Spring-mass oscillator
A mass m on a spring of constant k oscillates with T = 2π√(m/k). At the equilibrium position (natural length), there is no net force and the mass has maximum velocity. At maximum displacement (±A), the spring force is maximum (= kA) and the velocity is zero. The mass oscillates between +A and −A, passing through equilibrium every half period.
Worked Examples
Common Mistakes
- ⚠Using T = 2π√(k/m) instead of T = 2π√(m/k) — mass goes on top
- ⚠Thinking maximum velocity occurs at maximum displacement — it occurs at equilibrium (x = 0)