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

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

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

Steps: 4

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. The equation of motion involves mass (m), damping coefficient (b), spring constant (k), position (x), and time (t).
Step 3: Recognize that the equation describes how the position of the oscillator changes over time. It includes terms for acceleration (d²x/dt²), velocity (dx/dt), and position (x).
Step 4: Write down the general form of the equation. It is m d²x/dt² + b dx/dt + kx = 0, where each term represents a different aspect of the motion.