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What is the general form of the equation of motion for a damped oscillator?
What is the general form of the equation of motion for a damped oscillator?
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Q1
What is the general form of the equation of motion for a damped 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)
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The equation of motion for a damped oscillator includes a damping term (b dx/dt) along with the restoring force (kx).
Questions & Step-by-step Solutions
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Q
Q: What is the general form of the equation of motion for a damped oscillator?
Solution:
The equation of motion for a damped oscillator includes a damping term (b dx/dt) along with the restoring force (kx).
Steps: 5
Show Steps
Step 1: Understand that a damped oscillator is a system that loses energy over time due to friction or resistance.
Step 2: Recognize that the motion of the oscillator can be described by an equation.
Step 3: The general form of the equation includes a term for the restoring force, which is proportional to the displacement (kx).
Step 4: Add a damping term to the equation, which is proportional to the velocity (b dx/dt).
Step 5: Combine these terms to write the complete equation of motion for a damped oscillator: m(d²x/dt²) + b(dx/dt) + kx = 0.
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