A vibrating system has weight W = 4000 lb and a spring stiffness coefficient k = 10,000 lb/in. It has been determined experimentally that the logarithmic decrement Δ = 0.314 and the time between successive maximum Td = 0.2025s for the system.
Determine the following for the system in the given units:
a) The natural undamped frequency (rad/s)
b) The critical damping (lb · s/in)
c) The damping coefficient (lb · s/in)
d) The number of cycles and the time (s) required for the amplitude of motion to be reduced from an initial value of 0.1 in to 0.01 in. Hint: use log properties and the ratios of successive peak amplitudes.