logarithmic decrement proof

The video tutorial explains logarithmic decrement, an experimental method to determine the dampening ratio in underdamped systems. It revisits the concept of underdamped motion using a spring-mass-dampener system and derives the equation of motion. The tutorial defines delta as the natural logarithm of the ratio of successive amplitudes and simplifies the expression to find the dampening ratio. The video concludes by highlighting the importance of logarithmic decrement in understanding vibrations and determining the dampening constant.

Define delta in the context of logarithmic decrement.

What is the relationship between the damped period and the time between peaks in underdamped motion?

How can the dampening ratio be expressed in terms of delta?

What is the final result for the dampening ratio derived in the video?