What is the equation of motion for a damped harmonic oscillator?

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Q: What is the equation of motion for a damped harmonic oscillator?

Solution: The equation of motion for a damped harmonic oscillator is m d²x/dt² + b dx/dt + kx = 0.

Steps: 5

Step 1: Understand what a damped harmonic oscillator is. It is a system that experiences oscillations (like a swinging pendulum) but loses energy over time due to damping (like friction).
Step 2: Identify the components of the equation. 'm' is the mass of the object, 'b' is the damping coefficient, 'k' is the spring constant, 'x' is the displacement from the equilibrium position, and 't' is time.
Step 3: Recognize that the equation describes how the position 'x' changes over time due to the forces acting on the mass.
Step 4: Write down the equation: m d²x/dt² + b dx/dt + kx = 0. This means that the sum of the forces (mass times acceleration, damping force, and spring force) equals zero.
Step 5: Understand that d²x/dt² is the acceleration, dx/dt is the velocity, and kx is the restoring force from the spring.