Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Question
Chapter 12, Problem 12.7P
To determine
The characteristic frequencies and normal modes of the given system.
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Students have asked these similar questions
Consider a simple harmonic oscillator consisting of a one kilogram mass m' on a spring with spring/forceconstant k and length L'. If the mass of the spring ms is 9% of the attached mass, and k = 66 N/m,and if we determined the attached body is displaced 3 cm and given a downward velocity of 0.4 m/s -calculate,→ the frequency ω of the motion, ,→ and the amplitude A of the motion
Prove that using x(t) = Asin (ωt + ϕ) will produce the same results for the period for the oscillations of a mass and a spring. Why do you think the cosine function was chosen?
The maximum velocity attained by the mass of a simple harmonic oscillator is
10 cm/s, and the period of oscillation is 2 s. If the mass is released with an
initial displacement of 2 cm, find (a) the amplitude, (b) the initial velocity, (c)
the maximum acceleration, and (d) the phase angle.
Chapter 12 Solutions
Classical Dynamics of Particles and Systems
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Similar questions
- Show that, if a driven oscillator is only lightly damped and driven near resonance, the Q of the system is approximately Q2(TotalenergyEnergylossduringoneperiod)arrow_forwardProve that using x(t)=Asin(t+) will produce the same results for the period for the oscillations of a mass and a spring. Why do you think the cosine function was chosen?arrow_forwardPlot a velocity resonance curve for a driven, damped oscillator with Q = 6, and show that the full width of the curve between the points corresponding to is approximately equal to ω0/6.arrow_forward
- Let the initial position and speed of an overdamped, nondriven oscillator be x0 and v0, respectively. (a) Show that the values of the amplitudes A1 and A2 in Equation 3.44 have the values A1=2x0+v021 and A2=1x0+v021 where 1 = 2 and 2 = + 2. (b) Show that when A1 = 0, the phase paths of Figure 3-11 must be along the dashed curve given by x=2x, otherwise the asymptotic paths are along the other dashed curve given by x=1x. Hint: Note that 2 1 and find the asymptotic paths when t .arrow_forwardObtain the response of a linear oscillator to a step function and to an impulse function (in the limit τ → 0) for overdamping. Sketch the response functions.arrow_forward
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