Whcih type of function can be used to describe the amplitude of free damped vibration?

Question

BlackTom AI · Accepted Answer

To approach the question, consider how the amplitude behaves in a free damped vibration system.
Option 1: Periodic — this would imply a repeating, unchanged pattern like a sine or cosine wave, which does not account for the gradual loss of energy due to damping. Therefore, periodic is not appropriate for describing amplitude decay in a damped system.
Option 2: Exponential — in a damped oscillator, the envelope of the oscillation amplitude decays roughly as an exponential function of time, A(t) ≈ A0 e^(−ζωn t) for underdamped cases, or similar exponential forms in other damping regimes. This captures the observed rapid decrease in amplitude over time.
Option 3: Linear — a linear decay would imply a constant-rate drop in amplitude, which does not align with the physics of damping where the rate of energy loss leads to a multiplicative, not additive, decrease; thus linear is not an accurate descriptor.
Option 4: Polynomial — a polynomial decay would involve terms with powers of time that do not naturally model the standard damping behavior and can misrepresent the asymptotic approach to zero; damping is typically not well described by a polynomial envelope.
Overall, only the exponential form aligns with the well-established damping law governing free vibrations, where amplitude decreases multiplicatively over time due to energy dissipation.

INU1127 (24/25) Knowledge Check: Damping

Whcih type of function can be used to describe the amplitude of free damped vibration?

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