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Mechanical Engineering QUESTION #2440
Question 1
The logarithmic decrement \(\delta\) is used to experimentally measure damping. It is defined as:
  • \(\delta = \ln\frac{x(t)}{x(t+T_d)} = \frac{2\pi\alpha}{\omega_d} = \frac{2\pi\zeta}{\sqrt{1-\zeta^2}}\)✔️
  • \(\delta = \frac{x(t+T_d)}{x(t)}\)
  • \(\delta = \frac{\omega_d}{\alpha}\)
  • \(\delta = \frac{c}{2m}\)
Correct Answer Explanation
Logarithmic decrement: \(\delta=\ln\frac{x(t)}{x(t+T_d)}=\frac{2\pi\alpha}{\omega_d}=\frac{2\pi\zeta}{\sqrt{1-\zeta^2}}\). It allows \(\zeta\) to be determined from experiment.