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

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Question: What is the equation for the displacement of a damped harmonic oscillator?

Options:

Correct Answer: x(t) = A e^(-bt) cos(ωt)

Solution:

The displacement of a damped harmonic oscillator is given by x(t) = A e^(-bt) cos(ωt), where b is the damping coefficient.

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

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

Step 1: Understand that a damped harmonic oscillator is a system that oscillates but loses energy over time due to damping.
Step 2: Identify the key components of the equation: 'x(t)' represents the displacement at time 't', 'A' is the initial amplitude, 'b' is the damping coefficient, and 'ω' is the angular frequency.
Step 3: Recognize that the term 'e^(-bt)' represents the exponential decay of the amplitude due to damping.
Step 4: Note that 'cos(ωt)' describes the oscillatory motion of the system.
Step 5: Combine these components to form the complete equation: x(t) = A e^(-bt) cos(ωt).

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