PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
6th Edition
ISBN: 9781429206099
Author: Tipler
Publisher: MAC HIGHER
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Chapter 14, Problem 30P
(a)
To determine
The phase constant when the equation of the particle is given at
(b)
To determine
The phase constant when the equation of the particle is given at
(c)
To determine
The phase constant when the equation of the particle is given at
(d)
To determine
The phase constant when the equation of the particle is given atposition
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the general solution to a harmonic oscillator are
related.
There are two common forms for the general
solution for the position of a harmonic oscillator as
a function of time t:
1. x(t) = A cos (wt + p) and
2. x(t) = C cos (wt) + S sin (wt).
Either of these equations is a general solution of a
second-order differential equation (F= mā);
hence both must have at least two--arbitrary
constants--parameters that can be adjusted to fit
the solution to the particular motion at hand. (Some
texts refer to these arbitrary constants as boundary
values.)
Part D
Find analytic expressions for the arbitrary constants A and in Equation 1 (found in Part A) in terms of the constants C and Sin
Equation 2 (found in Part B), which are now considered as given parameters.
Express the amplitude A and phase (separated by a comma) in terms of C and S.
► View Available Hint(s)
Α, φ =
V
ΑΣΦ
?
A body of mass m is suspended by a rod of length L that pivots without friction (as shown). The mass is slowly lifted along a circular arc to a height h.
a. Assuming the only force acting on the mass is the gravitational force, show that the component of this force acting along the arc of motion is F = mg sin u.
b. Noting that an element of length along the path of the pendulum is ds = L du, evaluate an integral in u to show that the work done in lifting the mass to a height h is mgh.
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 F/SCI.+ENGRS.,STAND.-W/ACCESS
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