Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 10.5, Problem 24PS
To determine
To find the tangential component of acceleration at indicated time if the speed
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6.
Determine the amplitude of the function y = -4 sinx-7.
а.
7
с.
4
b. -7
d. -4
7. The period of the equation of motion given by x(t) = 6 sin (4nt) is
( a) πS
(b) 2 s
1
(c)
(d) 0.5 s
8. The frequency of the motion in (7) is
(a) - cycle
(b) 2 суcle
(с) 0.5 суcle
(d) 4п сусle
9. The amplitude of the motion in (7) is
(а) 4л
(b) 6
(c) 24 T
(d) None of the above
4. A car supported by a MacPherson strut (shock absorber system) travels on a bumpy
road at a constant velocity v. The equation modeling the motion of the car is
Tut
80x + 1000x
= 2500 cos
where r = x (t) represents the vertical position of the cars axle relative to its equilib-
rium position, and the basic units of measurement are feet and feet per second (this
is actually just an example of a forced, un-damped harmonic oscillator, if that is any
help). The constant numbers above are related to the characteristics of the car and
the strut. Note that the coefficient of time t (inside the cosine) in the forcing term
on the right hand side is a frequency, which in this case is directly proportional to the
velocity v of the car.
(a) Find the general solution to this nonhomogeneous ODE. Note that your answer
will have a term in it which is a function of v.
Chapter 10 Solutions
Calculus
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