Topic: Theory of Machines and Vibrations
Under logarithmic decrement, the amplitude of successive vibrations are
- A. Constant
- B. In arithmetic progression
- C. In geometric progression
- D. In logarithmic progression
Answer: C. In geometric progression
Explanation: The ratio of two successive oscillation amplitudes is constant in an underdamped system. The natural logarithm of this ratio is called logarithmic decrement $\delta = \ln\frac{x_{1}}{x_{2}} = \ln\frac{x_{2}}{x_{3}} \implies \frac{x_{1}}{x_{2}} = \frac{x_{2}}{x_{3}} \implies x_{2}^{2} = x_{1} \cdot x_{3}$. Hence, the amplitudes of successive vibrations are in a geometric progression.