A mass m oscillates on a spring with spring constant k, with amplitude d. At the moment when the mass is at position x = d/2, and moving in the +x direction (let this be when t = 0), a second mass 2m falls onto the first mass from above and sticks to it. Momentum is conserved in the x direction, but energy is not. (c) Write an expression for the energy lost in the collision in terms of d and k. (d) If after the collision the oscillator is subject to a damping force -bv and a drive force F0cos(ωt), find the drive frequency (in terms of the natural frequency ω0) which will return the oscillator to the original amplitude d.
A mass m oscillates on a spring with spring constant k, with amplitude d. At the moment when the mass is at position x = d/2, and moving in the +x direction (let this be when t = 0), a second mass 2m falls onto the first mass from above and sticks to it. Momentum is conserved in the x direction, but energy is not. (c) Write an expression for the energy lost in the collision in terms of d and k. (d) If after the collision the oscillator is subject to a damping force -bv and a drive force F0cos(ωt), find the drive frequency (in terms of the natural frequency ω0) which will return the oscillator to the original amplitude d.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A mass m oscillates on a spring with spring constant k, with amplitude d. At the moment when the mass is at position x = d/2, and moving in the +x direction (let this be when t = 0), a second mass 2m falls onto the first mass from above and sticks to it. Momentum is conserved in the x direction, but energy is not.
(c) Write an expression for the energy lost in the collision in terms of d and k.
(d) If after the collision the oscillator is subject to a damping force -bv and a drive force F0cos(ωt), find the drive frequency (in terms of the natural frequency ω0) which will return the oscillator to the original amplitude d.
Transcribed Image Text:2m
ww
m
x=0
x=d/2
X=d
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