Sects. 12.1 through 12.2

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Transcript Sects. 12.1 through 12.2

Chapter 12 – part A
The kinematics and dynamics of the
Simple Harmonic Oscillator
Summary

Kinematics

The motion
Dynamics
Important relations
T
A
Other important quantities
Exercise 12.4
4.
A particle moves in simple
harmonic motion with a frequency of
3.00 Hz and an amplitude of 5.00 cm.
(a) Through what total distance does
the particle move during one cycle of its
motion? (b) What is its maximum
speed? Where does this maximum
speed occur? (c) Find the maximum
acceleration of the particle. Where in
the motion does the maximum
acceleration occur?
Exercise 12.6
6.
A particle moves along the x
axis. It is initially at the position 0.270 m,
moving with velocity 0.140 m/s and
acceleration –0.320 m/s2. First, assume
that it moves with constant acceleration
for 4.50 s. Find (a) its position and (b) its
velocity at the end of this time interval.
Next, assume that it moves with simple
harmonic motion for 4.50 s and that x =
0 is its equilibrium position. Find (c) its
position and (d) its velocity at the end of
this time interval.
Exercise 12.8
8.
A simple harmonic oscillator
takes 12.0 s to undergo five complete
vibrations. Find (a) the period of its
motion, (b) the frequency in hertz, and
(c) the angular frequency in radians per
second.
Exercise 12.11
11.
A 0.500-kg object attached
to a spring with a force constant of
8.00 N/m vibrates in simple
harmonic motion with an amplitude
of 10.0 cm. Calculate (a) the
maximum value of its speed and
acceleration, (b) the speed and
acceleration when the object is 6.00
cm from the equilibrium position,
and (c) the time interval required for
the object to move from x = 0 to
x = 8.00 cm.
Exercise 12.12
12.
A 1.00-kg glider attached to a
spring with a force constant of 25.0 N/m
oscillates on a horizontal, frictionless air
track. At t = 0, the glider is released from
rest at x = –3.00 cm (that is, the spring is
compressed by 3.00 cm). Find (a) the
period of its motion, (b) the maximum
values of its speed and acceleration, and
(c) the position, velocity, and acceleration
as functions of time.
77.
Figure P10.77 shows a vertical
force applied tangentially to a uniform
cylinder of weight Fg. The coefficient of
static friction between the cylinder and
all surfaces is 0.500. In terms of Fg, find
the maximum force P that can be
applied that does not cause the cylinder
to rotate. (Suggestion: When the
cylinder is on the verge of slipping, both
friction forces are at their maximum
values. Why?)
76.
A solid sphere of mass m and
radius r rolls without slipping along the
track shown in Figure P10.76. It starts
from rest with the lowest point of the
sphere at height h above the bottom of
the loop of radius R, much larger than
r. (a) What is the minimum value of h
(in terms of R) such that the sphere
completes the loop? (b) What are the
force components on the sphere at the
point P if h = 3R?