Question

How do you find the amplitude of a simple harmonic oscillator?

Hint:

The amplitude of a simple harmonic oscillator is the maximum displacement from the equilibrium position and can be found using the energy equation \( A = \sqrt{\frac{2E}{k}} \).

Answer 1

The amplitude \( A \) of a simple harmonic oscillator is determined by the system's total mechanical energy. Total energy \( E \) comprises potential and kinetic energy, expressed as:\[E = \frac{1}{2} k A^2.\]Rearranging to solve for \( A \) yields:\[A = \sqrt{\frac{2E}{k}}.\]Consequently, the amplitude \( A \) is directly proportional to the total energy \( E \) and inversely proportional to the spring constant \( k \).