Frequency Amplitude and Period for underdamped motion summary

The video tutorial explains underdamped motion in a spring mass damper system. It introduces the equation of motion, X = a E to the minus Zeta Omega NT times sine Omega DT plus Phi, and describes how the amplitude decays exponentially. The tutorial also defines the damped period (TD) and frequency (FD), providing formulas for these concepts: TD = 1/FD and Omega D = 2π FD.

What is the equation of motion for a spring mass damper system in the underdamped case?

Explain the significance of the amplitude in the context of underdamped motion.

How is the damped period (T subscript D) calculated in a spring mass damper system?

Define the term 'damped frequency' and its relevance in the system.

What relationship exists between the damped frequency (FD) and the damped period (TD)?