What is the general form of the equation of motion for a damped harmonic oscilla
Practice Questions
Q1
What is the general form of the equation of motion for a damped harmonic oscillator?
m d²x/dt² + b dx/dt + kx = 0
m d²x/dt² + kx = 0
m d²x/dt² + b dx/dt = 0
m d²x/dt² + b dx/dt + kx = F(t)
Questions & Step-by-Step Solutions
What is the general form of the equation of motion for a damped harmonic oscillator?
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.
