Define logarithmic decrement. Derive a formula to calculate it
Answers
Answer:
1. Logarithmic decrement is used to find the damping ratio of an underdamped system in the time domain.
The method of logarithmic decrement becomes less and less precise as the damping ratio increases past about 0.5; it does not apply at all for a damping ratio greater than 1.0 because the system is overdamped.
2. To calculate logarithmic decrement, follow the given steps:
#The first step is to calculate the ratio of amplitudes.
#The third step is to calculate the logarithmic decrement. The logarithmic decrement is equal to the natural log of the ratio of the amplitudes.
#The fourth step is to calculate the damping factor. The damping factor is equal to the logarithmic decrement divided by the square root of 4 times pi squared plus the logarithmic decrement squared.
Step-by-step explanation:
Logarithmic decrement, {\displaystyle \delta }\delta , is used to find the damping ratio of an underdamped system in the time domain.
The method of logarithmic decrement becomes less and less precise as the damping ratio increases past about 0.5; it does not apply at all for a damping ratio greater than 1.0 because the system is overdamped.