Problems15 - Chapter 15 Problems 1, 2, 3 = straightforward,...
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Chapter 15 Problems
= straightforward, intermediate,
: Neglect the mass of every spring, except
in problems 66 and 68.
Section 15.1 Motion of an Object Attached to
Problems 15, 16, 19, 23, 56, and 62 in Chapter
7 can also be assigned with this section.
A ball dropped from a height of
4.00 m makes a perfectly elastic collision with
the ground. Assuming no mechanical energy is
lost due to air resistance, (a) show that the
ensuing motion is periodic and (b) determine the
period of the motion. (c) Is the motion simple
Section 15.2 Mathematical Representation of
Simple Harmonic Motion
In an engine, a piston oscillates with
simple harmonic motion so that its position
varies according to the expression
= (5.00 cm) cos(2
is in centimeters and
is in seconds. At
= 0, find (a) the position of the piston, (b) its
velocity, and (c) its acceleration. (d) Find the
period and amplitude of the motion.
The position of a particle is given by the
= (4.00 m) cos(3.00
is in meters and
is in seconds.
Determine (a) the frequency and period of the
motion, (b) the amplitude of the motion, (c) the
phase constant, and (d) the position of the
= 0.250 s.
(a) A hanging spring stretches by 35.0
cm when an object of mass 450 g is hung on it
at rest. In this situation, we define its position
= 0. The object is pulled down an
additional 18.0 cm and released from rest to
oscillate without friction. What is its position
at a time
84.4 s later? (b)
A hanging spring
stretches by 35.5 cm when an object of mass
440 g is hung on it at rest. We define this new
= 0. This object is also pulled
down an additional 18.0 cm and released from
rest to oscillate without friction. Find its
position 84.4 s later. (c) Why are the answers to
(a) and (b) different by such a large percentage
when the data are so similar? Does this
circumstance reveal a fundamental difficulty in
calculating the future? (d) Find the distance
traveled by the vibrating object in part (a). (e)
Find the distance traveled by the object in part
A particle moving along the
simple harmonic motion starts from its
equilibrium position, the origin, at
= 0 and
moves to the right. The amplitude of its motion
is 2.00 cm and the frequency is 1.50 Hz. (a)
Show that the position of the particle is given by
= (2.00 cm) sin(3.00
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