Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
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Chapter 14, Problem 99P
To determine
To show that the oscillation frequency is given by
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If we attach two blocks that have masses m1 and m2 to either end of a spring that has a force constant k and set them into oscillation by releasing them from rest with the spring stretched, show that the oscillation frequency is given by v = (k/m)^1/2, where m = m1m2 /(m1 + m2) is the reduced mass of the system.
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Problem 1:
A mass of 20 grams stretches a spring by 10/169 meters.
(a) Find the spring constant k, the angular frequency w, as well as the
period T and frequency f of free undamped motion for this spring-mass
system.
(b) Find the general solution x(t) of the DE for the free spring-mass
system.
(c) Suppose that an exterior force of
F(t) = 2.5 sin(12t) in Newtons
acts on the spring-mass system. Find the equation of motion (the solution
x(t)) of the system if the mass initially is at rest in its equilibrium position.
Show that the function x(t) = A cos ω1t oscillates with a frequency ν = ω1/2π. What is the
frequency of oscillation of the square of this function, y(t) = [A cos ω1t]2? Show that y(t) can also
be written as y(t) = B cos ω2t + C and find the constants B, C, and ω2 in terms of A and ω1
Chapter 14 Solutions
Physics for Scientists and Engineers, Vol. 1
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