A mass weighing 16 lb stretches a spring 3 in. The mass is attached to aviscous damper with a damping constant of 2 lb-s/ft. If the mass is setin motion from its equilibrium position with a downward velocity of 3in/s, find the position of the mass at any time t. Determine thequasi-frequency and quasi-period. Is the system critically damped,overdamped, or underdamped?

We have to find the position of the mass at any time t. We have to Determine the quasi-frequency and…

Answered: A mass weighing 16 lb stretches a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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An object stretches a spring 6 inches in equilibrium. a) Find its displacement for t > 0 if it is initially displaced 4 inches below equilibrium and given an upward velocity of 8 ft/s. y(t) = = b) State the natural frequency of the oscillation. Wo = rad/s c) State the period of the oscillation. T S = d) State the amplitude of the oscillation. R ft = e) State the phase angle of the oscillation. The phase angle should be between - T and π radians. = Notes: 1. Use g 32 ft/s². = rad 2. Assume there is no damping in the system and displacement and velocity are positive upward.
The following equation describes the motion of a mass on a spring subject to damping, with a coefficient of friction c > 0: 2.1" + cr' + 3x = 0. For which values of c > 0 is the system: (b) Overdamped?
8 A mass weighing 16 pounds stretches a spring feet. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s² for the acceleration due to gravity.) 2 (√4) x(1) - e -(5) [ - 14 cos (1) ( (VT),) - 134 sin(e) ((7),)] + 20 cos (3) +- 20 sin (38) = е 3 2 3√4t 2 3 3 ft
*) Find y as a function of x if y" 11y" + 18y' = 32e*, y(0) = 29, y'(0) = 12, y"(0) = 22. y(x) =
It takes 15 J of work to stretch a spring 0.2 m from its equilibrium position. Find the spring constant k. (Hint: read the units!) How far would the spring need to be stretched in order to do twice the amount of work?
4.4 11 11. A 0.2-kg mass is attached to a spring having a spring constant 5 kg/s2. The system is displaced 0.5 m from its equilibrium position and released from rest. If there is no damping present, find the amplitude, frequency, and phase of the resulting motion. Plot the solution.

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