What is the equation for the displacement of a damped harmonic oscillator?
Practice Questions
1 question
Q1
What is the equation for the displacement of a damped harmonic oscillator?
x(t) = A e^(-bt) cos(ωt)
x(t) = A e^(bt) cos(ωt)
x(t) = A cos(ωt)
x(t) = A e^(-bt) sin(ωt)
The displacement of a damped harmonic oscillator is given by x(t) = A e^(-bt) cos(ωt), where b is the damping coefficient.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the equation for the displacement of a damped harmonic oscillator?
Solution: The displacement of a damped harmonic oscillator is given by x(t) = A e^(-bt) cos(ωt), where b is the damping coefficient.
Steps: 5
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).
