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Questions and Answers
What is the expression for the energy at time t in damping motion?
What is the expression for the energy at time t in damping motion?
- E(t) = Eo e^{-2bt} (correct)
- E(t) = Eo e^{bt}
- E(t) = Eo e^{2bt}
- E(t) = Eo e^{-bt}
What is the expression for the logarithmic decrement of amplitude of a damped oscillator?
What is the expression for the logarithmic decrement of amplitude of a damped oscillator?
- ln(Ad) = ln(P) * bt
- ln(Ad) = ln(P) / bt
- ln(Ad) = ln(P) + bt
- ln(Ad) = ln(P) - bt (correct)
What is the relationship between successive amplitudes A3 and A4 of a damped oscillator?
What is the relationship between successive amplitudes A3 and A4 of a damped oscillator?
- A4 = Ao e^{-b(3T+T/4)} (correct)
- A4 = Ao e^{-b(2T+T/4)}
- A4 = Ao e^{-bT/4}
- A4 = Ao e^{-b(T+T/4)}
What does the constant ebT represent in the context of a damped oscillator?
What does the constant ebT represent in the context of a damped oscillator?
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At what time t does the amplitude A1 of a damped oscillator reach Ao e^{-bT/4} if the oscillator starts from its mean position?
At what time t does the amplitude A1 of a damped oscillator reach Ao e^{-bT/4} if the oscillator starts from its mean position?
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Study Notes
Simple Harmonic Motion (SHM)
- SHM is a type of periodic motion that repeats after a definite time interval.
- The amplitude of oscillation is small, and the damping is smaller than the oscillation frequency (b < ω).
Damped Oscillation
- The equation of motion for damped oscillation is x = e^(-bt) [A cos(ω² - b² t) + B sin(ω² - b² t)].
- The amplitude of oscillatory damped oscillation is not constant, but it dies away exponentially (P e^(-bt)).
- The oscillatory function is x = P e^(-bt) cos(ω² - b² t - ψ).
Undamped SHM
- When b = 0, the equation of motion becomes x = P cos(ωt - ψ), which is the solution for free/undamped SHM.
Conclusions
- The amplitude of oscillatory damped oscillation decreases exponentially with time.
- The frequency of oscillation is affected by the damping factor (b).
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