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 can be found using the total mechanical energy of the system. The total energy \( E \) is the sum of potential and kinetic energy: \[ E = \frac{1}{2} k A^2. \] Solving for \( A \), we get: \[ A = \sqrt{\frac{2E}{k}}. \] Thus, the amplitude \( A \) is related to the total energy \( E \) and the spring constant \( k \).