a mass weighing 16lb streches a spring 3in. the mass is attached to a viscous damper with a damping contanat of 2 lb * s

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a mass weighing 16lb streches a spring 3in. the mass is attached to a viscous damper with a damping contanat of 2 lb * s/ft.
find the logarithmic decrement of the system.
round answer to 3 decimal places

A Mass Weighing 16lb Streches A Spring 3in The Mass Is Attached To A Viscous Damper With A Damping Contanat Of 2 Lb S 1 (82.15 KiB) Viewed 55 times

For the damped oscillation described by U= Re-y/2m cos(ut - 8), the time between successive maxima is Ta 2TT μ The ratio of the displacements at two successive maxima is given by exp (yd) 2m Observe that this ratio does not depend on which pair of maxima is chosen. The natural logarithm of this ratio is called the logarithmic decrement and is denoted by A. A= πγ mu Since m, μ, and A are quantities that can be measured easily for a mechanical system, this result provides a convenient and practical method for determining the damping constant of the system, which is more difficult to measure directly. In particular, for the motion of a vibrating mass in a viscous fluid, the damping constant depends on the viscosity of the fluid; for simple geometric shapes the form of this dependence is known, and the preceding relation allows the experimental determination of the viscosity. This is one of the most accurate ways of determining the viscosity of a gas at high pressure. A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a damping constant of 2 lbs/ft. Find the logarithmic decrement of the system. (A computer algebra system is recommended. Round your answer to four decimal places.)