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
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdad547ee-b0cc-45e8-9aec-d7dc8028defe%2Fb92647a4-9303-4d4c-b93a-e749dc2af020%2Fnieak1j_processed.jpeg&w=3840&q=75)
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