PERIODIC MOTION
Many kinds of motion repeat themselves over and over: the vibration of a quartz crystal in a watch, the swinging pendulum of a grandfather clock, the sound vibrations produced by a clarinet or an organ pipe, and the back-and-forth motion of the pistons in a car engine. This kind of motion, called periodic motion or oscillation, is the subject of this chapter. Understanding periodic motion will be essential for our later study of waves, sound, alternating electric currents, and light.
A body that undergoes periodic motion always has a stable equilibrium position. When it is moved away from this position and released, a force or torque comes into play to pull it back toward equilibrium. But by the time it gets there, it has picked up some kinetic energy, so it overshoots, stopping somewhere on the other side, and is again pulled back toward equilibrium. Picture a ball rolling back and forth in a round bowl or a pendulum that swings back and forth past its straight-down position.
In this chapter we will concentrate on two simple examples of systems that can undergo periodic motions: spring-mass systems and pendulums. We will also study why oscillations often tend to die out with time and why some oscillations can build up to greater and greater displacements from equilibrium when periodically varying forces act.
Frequently Asked Questions
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Ans: HERE ISA SUMMARY OF GRAVITATION , FOR QUICK REVISION view more..
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Ans: If light cannot escape from a black hole and if black holes are small
. how can we know that such things exist? The answer is
that any gas or dust near the black hole tends to be pulled into an accretion disk
that swirls around and into the black hole, rather like a whirlpool view more..
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Ans: At points far from a black hole, its gravitational effects are the same as those
of any normal body with the same mass. If the sun collapsed to form a black
hole, the orbits of the planets would be unaffected. But things get dramatically
different close to the black hole. view more..
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Ans: Many kinds of motion repeat themselves over and over: the vibration of
a quartz crystal in a watch, the swinging pendulum of a grandfather
clock, the sound vibrations produced by a clarinet or an organ pipe,
and the back-and-forth motion of the pistons in a car engine. This kind of motion,
called periodic motion or oscillation view more..
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Ans: n. A body with mass m rests on a frictionless horizontal guide system, such
as a linear air track, so it can move along the x-axis only. The body is attached to
a spring of negligible mass that can be either stretched or compressed. The left
end of the spring is held fixed, and the right end is attached to the body. The
spring force is the only horizontal force acting on the body; the vertical normal
and gravitational forces always add to zero view more..
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Ans: Here are some terms that we’ll use in discussing periodic motions of all kinds: view more..
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Ans: The simplest kind of oscillation occurs when the restoring force Fx is directly
proportional to the displacement from equilibrium x. This happens if the spring
in Figs. 14.1 and 14.2 is an ideal one that obeys Hooke’s law view more..
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Ans: To explore the properties of simple harmonic motion, we must express the displacement
x of the oscillating body as a function of time, x1t2. view more..
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Ans: the period and frequency of simple harmonic
motion are completely determined by the mass m and the force constant k.
In simple harmonic motion the period and frequency do not depend on the
amplitude A. view more..
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Ans: We still need to find the displacement x as a function of time for a harmonic
oscillator. Equation (14.4) for a body in SHM along the x-axis is identical to
Eq. (14.8) for the x-coordinate of the reference point in uniform circular motion
with constant angular speed v = 2k/m view more..
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Ans: We can learn even more about simple harmonic motion by using energy considerations.
The only horizontal force on the body in SHM in Figs. 14.2 and 14.13 is
the conservative force exerted by an ideal spring. The vertical forces do no work,
so the total mechanical energy of the system is conserved. We also assume that
the mass of the spring itself is negligible. view more..
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Ans: the energy quantities E, K, and U at x = 0, x = ±A/2, and
x = ±A. Figure 14.15 is a graphical display of Eq. (14.21); energy (kinetic,
potential, and total) is plotted vertically and the coordinate x is plotted horizontally.
The parabolic curve in Fig. 14.15a represents the potential energy U = 1/2 kx2
. The
horizontal line represents the total mechanical energy E, which is constant and
does not vary with x. view more..
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Ans: PROBLEM SOLVING STRATEGY ON ENERGY MOMENTUM OF SHM view more..
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Ans: So far, we’ve looked at a grand total of one situation in which simple harmonic
motion (SHM) occurs: a body attached to an ideal horizontal spring. But SHM
can occur in any system in which there is a restoring force that is directly proportional
to the displacement from equilibrium, as given by Eq. (14.3), Fx = -kx view more..
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Ans: A mechanical watch keeps time based on the oscillations of a balance wheel
(Fig. 14.19). The wheel has a moment of inertia I about its axis. A coil spring
exerts a restoring torque tz that is proportional to the angular displacement u
from the equilibrium position. We write tz = -ku, where k (the Greek letter
kappa) is a constant called the torsion constant. Using the rotational analog
of Newton’s second law for a rigid body, gtz = Iaz = I d2
u>dt2
view more..
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Ans: The following discussion of the vibrations of molecules uses the binomial theorem.
If you aren’t familiar with this theorem, you should read about it in the appropriate
section of a math textbook.
view more..
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Ans: A simple pendulum is an idealized model consisting of a point mass suspended
by a massless, unstretchable string. When the point mass is pulled to one side of
its straight-down equilibrium position and released, it oscillates about the equilibrium
position. view more..
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Ans: A physical pendulum is any real pendulum that uses an extended body, as contrasted
to the idealized simple pendulum with all of its mass concentrated at a
point. F view more..
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