# 15.2 Energy in simple harmonic motion  (Page 3/8)

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## Oscillations about an equilibrium position

We have just considered the energy of SHM as a function of time. Another interesting view of the simple harmonic oscillator is to consider the energy as a function of position. [link] shows a graph of the energy versus position of a system undergoing SHM.

The potential energy curve in [link] resembles a bowl. When a marble is placed in a bowl, it settles to the equilibrium position at the lowest point of the bowl $\left(x=0\right)$ . This happens because a restoring force    points toward the equilibrium point. This equilibrium point is sometimes referred to as a fixed point . When the marble is disturbed to a different position $\left(x=+A\right)$ , the marble oscillates around the equilibrium position. Looking back at the graph of potential energy, the force can be found by looking at the slope of the potential energy graph $\left(F=-\frac{dU}{dx}\right)$ . Since the force on either side of the fixed point points back toward the equilibrium point, the equilibrium point is called a stable equilibrium point    . The points $x=A$ and $x=\text{−}A$ are called the turning points . (See Potential Energy and Conservation of Energy .)

Stability is an important concept. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. The stable equilibrium point occurs because the force on either side is directed toward it. For an unstable equilibrium point, if the object is disturbed slightly, it does not return to the equilibrium point.

Consider the marble in the bowl example. If the bowl is right-side up, the marble, if disturbed slightly, will oscillate around the stable equilibrium point. If the bowl is turned upside down, the marble can be balanced on the top, at the equilibrium point where the net force is zero. However, if the marble is disturbed slightly, it will not return to the equilibrium point, but will instead roll off the bowl. The reason is that the force on either side of the equilibrium point is directed away from that point. This point is an unstable equilibrium point.

[link] shows three conditions. The first is a stable equilibrium point (a), the second is an unstable equilibrium point (b), and the last is also an unstable equilibrium point (c), because the force on only one side points toward the equilibrium point.

The process of determining whether an equilibrium point is stable or unstable can be formalized. Consider the potential energy curves shown in [link] . The force can be found by analyzing the slope of the graph. The force is $F=-\frac{dU}{dx}.$ In (a), the fixed point is at $x=0.00\phantom{\rule{0.2em}{0ex}}\text{m}\text{.}$ When $x<0.00\phantom{\rule{0.2em}{0ex}}\text{m,}$ the force is positive. When $x>0.00\phantom{\rule{0.2em}{0ex}}\text{m,}$ the force is negative. This is a stable point. In (b), the fixed point is at $x=0.00\phantom{\rule{0.2em}{0ex}}\text{m}\text{.}$ When $x<0.00\phantom{\rule{0.2em}{0ex}}\text{m,}$ the force is negative. When $x>0.00\phantom{\rule{0.2em}{0ex}}\text{m,}$ the force is also negative. This is an unstable point.

A force F is needed to break a copper wire having radius R. The force needed to break a copper wire of radius 2R will be
2F
Jacob
The difference between vector and scaler quantity
vector has both magnitude & direction but scalar has only magnitude
Manash
my marunong ba dto mag prove ng geometry
ron
how do I find resultant of four forces at a point
Inusah
use the socatoa rule
kingsley
draw force diagram, then work out the direction of force.
Rongfang
In a closed system of forces... Summation of forces in any direction or plane is zero... Resolve if there is a need to then add forces in a particular plane or direction.. Say the x direction... Equate it tk zero
Jacob
define moment of inertia
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joining of two wire of different material forming two junctions. If one is hot and another is cold the it will produce emf...
joining of two metal of different materials to form a junction in one is hot & another is cold
Manash
define dimensional analysis
mathematical derivation?
Hira
explain what Newtonian mechanics is.
a system of mechanics based of Newton laws motion this is easy difenation of mean...
Arzoodan
what is the meaning of single term,mechanics?
jyotirmayee
mechanics is the science related to the behavior of physical bodies when some external force is applied to them
Lalita
SO ASK What is Newtonian mechanics in physics? Newtonian physics, also calledNewtonian or classical mechanics, is the description of mechanical events—those that involve forces acting on matter—using the laws of motion and gravitation formulated in the late seventeenth century by English physicist
Suleiman
can any one send me the best reference book for physics?
Prema
concept of physics by HC verma, Fundamentals of Physics, university of physics
tq u.
Prema
these are the best physics books one can fond both theory and applications.
can any one suggest best book for maths with lot of Tricks?
Vivek
what is the water height in barometer?
SUNEELL
13.5*76 cm. because Mercury is 13.5 times dense than Mercury
LOVE
water is 13.5 times dense than the Mercury
LOVE
plz tell me frnds the best reference book for physics along with the names of authors.
Prema
i recomended the reference book for physics from library University of Dublin or library Trinity college
Arzoodan
A little help here... . 1. Newton's laws of Motion, are they applicable to motions of all speeds? 2.state the speeds which are applicable to Newtons laws of Motion
Derek
mechanics which follows Newtons law
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The definition of axial and polar vector .
Arpita
polar vector which have a starting point or pt. of applications is,force,displacement
jyotirmayee
axial vector represent rotational effect and act along the axis of rotation b
jyotirmayee
explain the rule of free body diagram
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application of elasticity
good
Anwar
a boy move with a velocity of 5m/s in 4s. What is the distance covered by the boy?
What is the time required for the sun to reach the earth?
anthony
24th hr's, your question is amazing joke 😂
Arzoodan
velocity 20 m, s
Ahmed
the sun shines always and the earth rotates so the question should specify a place on earth and that will be 24hrs
Opoku
20m
Gabriel
good nice work
Anwar
20m
Evelyn
why 20?.
Arzoodan
v =distance/time so make distance the subject from the equation
Evelyn
20m
Olaide
exatly
Arzoodan
what is differemce between principles and laws
plz
Anwar
how can a 50W light bulb use more energy than a 1000W oven?
That depends on how much time we use them
Phrangsngi
It states that, " If two vectors are represented in magnitude and direction by the two sides of a triangle, then their resultant is represented in magnitude and direction by the third side of the triangl " .
Nabin
thanks yaar
Pawan
And it's formula
Pawan
Manash
plank constant is what
plank constant is a phisical constant that the central quantum
Arzoodan
links energy of a photon to it's wave length