29. A simple harmonic oscillator of amplitude A has a total energy E. Determine (a) the kinetic energy and (b) the potential energy when the position is one-third the amplitude. (c) For what values of the position does the kinetic energy equal one-half the potential energy? (d) Are there any values of the position where the kinetic energy is greater than the maximum potential energy? Explain. ens off a bridge

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Chapter13: Vibrations And Waves
Section: Chapter Questions
Problem 32P: A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is...
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475
476
Chapter 15 Oscillatory Motion
the speed
6.00 cm
me inter
0 to x
from rest from this stretched position, and it subse-
quently undergoes simple harmonic oscillations. Find
(a) the force constant of the spring, (b) the frequency
of the oscillations, and (c) the maximum speed of the
object. (d) Where does this maximum speed occur?
(e) Find the maximum acceleration of the object.
(f) Where does the maximum acceleration occur?
(g) Find the total energy of the oscillating system.
friction that would allow the block to reach t
librium position?
32. A 326-g object is attached to a spring and exec
AMT ple harmonic motion with a period of 0.256
total energy of the system is 5.83 J, find (a)
mum speed of the object, (b) the force cons
spring, and (c) the amplitude of the motion.
a hang-
tending
sibrating.
period?
object when its position is equal to one-third the max-
imum value.
n 15.4 Comparing Simple Harmonic Motion
with i iform Circular Motion
you can
33. W ile driving behind a car travel-
in at 3.00 m/s, you notice that one
Bu
tor
w-speed
o a brick
g with a
3.16 cm
wd of the
energy is
act with
29. A simple harmonic oscillator of amplitude A has a
total energy E. Determine (a) the kinetic energy and
(b) the potential energy when the position is one-third
the amplitude. (c) For what values of the position does
the kinetic energy equal one-half the potential energy?
(d) Are there any values of the position where the
kinetic energy is greater than the maximum potential
energy? Explain.
30. Review. A 65.0-kg bungee jumper steps off a bridge
GP with a light bungee cord tied to her body and to the
of he car's tires has a small hemi-
spl rical bump on its rim as shown
in gure P15.33. (a) Explain why the
bu p, from your viewpoint behind
the car, executes simple harmonic
me ion. (b) If the radii of the car's
tin are 0.300 m, what is the bump's
pe od of oscillation?
Sectio 15.5 The Pendulum
ched length of the cord is 11.0 m.
wing and
eriod of
oJ. Find
he anpli-
The jumper reaches the bottom v--
below the bridge before bouncing back. We wish to
find the time interval between her leaving the bridge
and her arriving at the bottom of her motion.
Her overall motion can be separated into an 11.0-m
free fall and a 25.0-m section of simple harmonic
oscillation. (a) For the free-fall part, what is the
appropriate analysis model to describe her motion?
(b) For what time interval is she in free fall? (c) For
the simple harmonic oscillation part of the plunge, is
olem 68 in Chapter 1 can also be assig
section.
34. A "seconds pendulum" is one that m
equilibrium position once each secone
the pendulum is precisely 2 s.) The le
pendulum is 0.992 7 m at Tokyo, Japa
at Cambridge, England. What is thes
fall accelerations at these two location
myle har
When the
n and
35. A simple pendulum makes 120 comp
3.00 min at a location where g-9.8
Tihe pendulum and (b) its
of ths bungee jumper, the spring, and the
Transcribed Image Text:475 476 Chapter 15 Oscillatory Motion the speed 6.00 cm me inter 0 to x from rest from this stretched position, and it subse- quently undergoes simple harmonic oscillations. Find (a) the force constant of the spring, (b) the frequency of the oscillations, and (c) the maximum speed of the object. (d) Where does this maximum speed occur? (e) Find the maximum acceleration of the object. (f) Where does the maximum acceleration occur? (g) Find the total energy of the oscillating system. friction that would allow the block to reach t librium position? 32. A 326-g object is attached to a spring and exec AMT ple harmonic motion with a period of 0.256 total energy of the system is 5.83 J, find (a) mum speed of the object, (b) the force cons spring, and (c) the amplitude of the motion. a hang- tending sibrating. period? object when its position is equal to one-third the max- imum value. n 15.4 Comparing Simple Harmonic Motion with i iform Circular Motion you can 33. W ile driving behind a car travel- in at 3.00 m/s, you notice that one Bu tor w-speed o a brick g with a 3.16 cm wd of the energy is act with 29. A simple harmonic oscillator of amplitude A has a total energy E. Determine (a) the kinetic energy and (b) the potential energy when the position is one-third the amplitude. (c) For what values of the position does the kinetic energy equal one-half the potential energy? (d) Are there any values of the position where the kinetic energy is greater than the maximum potential energy? Explain. 30. Review. A 65.0-kg bungee jumper steps off a bridge GP with a light bungee cord tied to her body and to the of he car's tires has a small hemi- spl rical bump on its rim as shown in gure P15.33. (a) Explain why the bu p, from your viewpoint behind the car, executes simple harmonic me ion. (b) If the radii of the car's tin are 0.300 m, what is the bump's pe od of oscillation? Sectio 15.5 The Pendulum ched length of the cord is 11.0 m. wing and eriod of oJ. Find he anpli- The jumper reaches the bottom v-- below the bridge before bouncing back. We wish to find the time interval between her leaving the bridge and her arriving at the bottom of her motion. Her overall motion can be separated into an 11.0-m free fall and a 25.0-m section of simple harmonic oscillation. (a) For the free-fall part, what is the appropriate analysis model to describe her motion? (b) For what time interval is she in free fall? (c) For the simple harmonic oscillation part of the plunge, is olem 68 in Chapter 1 can also be assig section. 34. A "seconds pendulum" is one that m equilibrium position once each secone the pendulum is precisely 2 s.) The le pendulum is 0.992 7 m at Tokyo, Japa at Cambridge, England. What is thes fall accelerations at these two location myle har When the n and 35. A simple pendulum makes 120 comp 3.00 min at a location where g-9.8 Tihe pendulum and (b) its of ths bungee jumper, the spring, and the
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