# Solved examples on SHM

EX 1

**Frequently Asked Questions**

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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: 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: 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: 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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