This document summarizes key concepts about simple harmonic motion:
1) Simple harmonic motion occurs when the acceleration of an object is proportional to and opposite of the displacement from a central point. The force causing the motion is called a restoring force.
2) Periodic variables that describe simple harmonic motion include amplitude, period, frequency, and angular frequency. The period is the time for one complete oscillation.
3) Examples of simple harmonic motion include a mass on a spring, the motion of a simple pendulum, and uniform circular motion. For a mass on a spring, the acceleration is proportional to the displacement from equilibrium.
4) Other types of oscillatory motion discussed include the simple pendulum and
This paper presents the Physics Rotational Method of the simple gravity pendulum, and it also applies Physics Direct Method to represent these equations, in addition to the numerical solutions discusses. This research investigates the relationship between angular acceleration and angle to find out different numerical solution by using simulation to see their behavior which shows in last part of this article.
This paper presents the Physics Rotational Method of the simple gravity pendulum, and it also applies Physics Direct Method to represent these equations, in addition to the numerical solutions discusses. This research investigates the relationship between angular acceleration and angle to find out different numerical solution by using simulation to see their behavior which shows in last part of this article.
this is class 12 Maharashtra board physics subject content. this is complete content with notes with easily explaination.
for buying or neet attractive ppt in any subject contact me 8879919898. go to my site akchem.tk
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This Unit is rely on introduction to Simple Harmonic Motion. the contents was prepared using the Curriculum of NTA level 4 at Mineral Resources Institute- Dodoma.
Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.
Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predatorβprey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. Contents
this is class 12 Maharashtra board physics subject content. this is complete content with notes with easily explaination.
for buying or neet attractive ppt in any subject contact me 8879919898. go to my site akchem.tk
blog akchem.blogspot.com
This Unit is rely on introduction to Simple Harmonic Motion. the contents was prepared using the Curriculum of NTA level 4 at Mineral Resources Institute- Dodoma.
Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.
Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predatorβprey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. Contents
Introduction to oscillations and simple harmonic motionMichael Marty
Β
Physics presentation about Simple Harmonic Motion of Hooke's Law springs and pendulums with derivation of formulas and connections to Uniform Circular Motion.
References include links to illustrative youtube clips and other powerpoints that contributed to this peresentation.
MAHARASHTRA STATE BOARD
CLASS XI AND XII
CHAPTER 5
OSCILLATIONS
CONTENT
Introduction
Periodic and oscillatory
motions
Simple harmonic motion
Simple harmonic motion
and uniform circular
motion
Velocity and acceleration
in simple harmonic motion
Force law for simple
harmonic motion
Energy in simple harmonic
motion
Some systems executing
simple harmonic motion
Damped simple harmonic
motion
Forced oscillations and
resonance
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
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In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Model Attribute Check Company Auto PropertyCeline George
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In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
How to Make a Field invisible in Odoo 17Celine George
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It is possible to hide or invisible some fields in odoo. Commonly using βinvisibleβ attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as βdistorted thinkingβ.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
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What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
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http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasnβt one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
1. 1
CHAPTER 2
SIMPLE HARMONIC MOTION
2.1 Definitionof SimpleHarmonicMotion
ο· Simple harmonicmotion, occurswhenthe accelerationisproportionaltodisplacementbutthey
are inopposite directions.
ο· Simple HarmonicMotion(SHM).The motionthatoccurs whenan objectisacceleratedtowards
a mid-point.The size of the accelerationisdependentuponthe distance of the objectfromthe
mid-point.Verycommontype of motion,eg.seawaves,pendulums,spring.
ο· Simple harmonicmotionoccurswhenthe force Facting onan objectisdirectlyproportional to
the displacementx of the object,butinthe opposite direction.
ο· Mathematical statementF= - kx
ο· The force iscalleda restoringforce because italwaysactson the objectto returnit to its
equilibriumposition.
2.2 Descriptive terms
a. The amplitude A isthe maximumdisplacementfromthe equilibriumposition.
b. The periodT isthe time forone complete oscillation.Aftertime Tthe motionrepeatsitself.In
general x(t) =x (t + T).
c. The frequencyf isthe numberof oscillationspersecond.The frequencyequalsthe reciprocal of
the period. f = 1/T.
d. Althoughsimple harmonicmotionisnotmotioninacircle,it isconvenienttouse angular
frequency bydefiningο·= 2pf = 2p/T
2.3 Simple HarmonicMotion
A bodyat simple harmonicmotionif :
a) The accelerationalwaysdirectedtowardafixedpointsontheirpath.
b) The accelerationisproportional toitsdisplacementfromafixedpointsandalwaysdirectedtoward
that points.
2. 2
Example forsimple harmonicmotion
a) When a mass hanging from the spring is deflected it will move with simple harmonic motion.
b) Motion of the piston in a cylinder is close simple harmonic motion.
c) Weight of the pendulum moves with simple harmonic motion if the angle is small.
4. 4
Figure 2.1 (i) shows a point P rotating with constant velocity ,ο· in a circular
path of radius , a
Linear velocity , V = aο·
From figure 2.1 (ii) , the horizontal component of velocity V , the velocity of point Q
Vq = V sin ο± = aο· sin ο±
From space diagram,
PQ = ο(a2 β x2)
ο sin ο± = ο(a2 - x2)
a
ο Vq = (aο·) ο(a2 - x2)
a
= (ο·) ο(a2 - x2)
P
V
ο·
O
,
Q
P , Q
X
P
V
ο·
O, Q
i) Vq maksimum=aο· ii) Vq minimum=0
Figure : 2.2
5. 5
Whenx = 0 , Vq ismaximum,
ο Vq maks = ο·ο(a2
β 0) = aο· (figure 2.2 i)
Whenx = a , Vq is minimum
ο Vq min= ο·ο(a2
β a2
) = 0 (figure 2.2 ii)
If P rotate with constant angular speed ο· , it also has a central
acceleration f , goes to center of rotation O.
f = a ο·2
o
P
V
a
X
Ο
Q
P
f = aο·2
f q
Q
0
(ii) Vectordiagram
P
Q0
a
x
(i)
Figure : 2.3
(iii) space diagram
6. 6
(fromfigure 2.3 ii : vectordiagram )
central acceleration of the horizontal component f , the acceleration of point Q
fq = a ο·2
kosο±
fromfigure 2.3 iii , kos ο± = x
a
ο fq = (a ο·2
) x
a
= x ο·2
Whenx = 0 , fq isminimum
ο fq min = 0ο·2
= 0
Whenx = a , fq is maximum
ο fq maks = a ο·2
2.5 PeriodicTime ,FrequencyandAmplitud
Periodic time or period , T is the time taken by the point Q to make a
swing back and forth to complete . And that time isequal to the time taken
by the OP toturn a rotation 2 ο° radians with angularspeed ο· rad/s .
ο Periodictime ,T= 2ο°
ο·
But , fq = xο·2
dan ο· = ο fq
X
ο T = 2ο° ο x = 2ο° ο distance
fq acceleration
7. 7
Frequency, n is the number of a complete cycle of oscillation in the
penetration by the point Q in the second. The unit is the Hertz ( Hz), ie
one cycle per second .
οFrequency , n = ο· Hz
2ο°
n = 1/T
=1______________ Hz
2ο°ο distance/acceleration
Amplitude , a is the maximum displacement of point Q from a fixed
point O. The distance , 2a traveled by the point Q is known as a
stroke or swing .
EXAMPLE 1
A point moves with simple harmonic motion with the acceleration of 9
m/s2 and velocity of 0.92 m/s when it is 65 mm from the center
of travel. Find :
i. amplitude ,
ii. time of the periodic motion
8. 8
EXAMPLE 2
A particle moving with simple harmonic motion has a periodic time of
0.4 s and it was back and forth between two points is 1.22 m.
Determine :
i. The frequency and amplitude of the oscillation .
ii. Velocity and acceleration of the particle when it is 400 mm from the
center of oscillation .
iii.Velocity and maximum acceleration of the movement .
EXAMPLE 3
A mass of body 1.5 kg moving with simple harmonic motion is towards
to the end of the swing . At the time he was at A, 760 mm from the
center of oscillation , velocity and acceleration is 9 m/s and 10 m/s2
, respectively. Find :
a) frequency and amplitude of the oscillation ,
b) the maximum acceleration and the inertia of the body when it is at
the end of the swing ,
c) the time has elapsed for it to go and back to A.
9. 9
2.6 Elastic system - mass and spring.
mg
d
Stiffnessof
spring,S
Ked.tak
tegang
Ked.tegang
dan pegun
Ked.keseim
bangan,o
Ked.terpesong
Daya spring
x
Mf
f
mg
10. 10
The figure shows a body of mass M kg supported by a spring of
stiffness S N/m . Static spring deflection is d meters , then:
Mg = Sd
If the body is in the pull- down x meters from the equilibrium position O
( a fixed point) and then released , so
Body weight + inertia force = total spring force
Mg + Mf = Sd + Sx
Where, Mg = Sd
ο Mf = Sx
f = (S/M) x
The reference S/M is constant for a system under consideration.
So , the acceleration f is proportional to the distance x from the
equilibrium position O . This indicates that the body is moving with simple
harmonic motion .
From SHM,
f = xο·2
οο·=
β
π
π
11. 11
So, time periodic , T = 2ο°
ο·
β΄ π = 2πβ
π
π
Mg = Sd dan π
π
= π
π
β΄ π = 2π β(
π
π
)
EXAMPLE 4
A body of mass 14 kg is suspended by springs up from the end
attached to a rigid support . The body produces a static deflection of
25 mm . It is in the pull down as far as 23 mm and then
released . Find :
i. Initial acceleration of the body ,
ii. the periodic time oscillations ,
iii. the maximum spring force ,
iv. the velocity and acceleration of the body when it is 12 mm
from the equilibrium position .
12. 12
EXAMPLE 5
Two body , each type per 6.5 kg , suspended on a vertical
spring with stiffness 2.45 kN/m. A body is removed and this causes
the system to oscillate. Find :
i. The maximum extension spring ,
ii. the periodic time and amplitude of the oscillation ,
iii. the velocity and acceleration of the mass when it is at the
center of the amplitude ,
iv. the total energy of the oscillations .
2.7 Simple pendulum
ο‘ , ο
Mff
ο¦
mg
mf
P
ο±
13. 13
The diagram shows a simple pendulum of length cord, L and weight B
with mass M. Amplitude of the oscillation ο¦ is small, not exceeding
120 , the angular displacement ο± and the three forces , the heavy weight ,
cord tension and inertia forces , is in equilibrium( figure ii) From the
force triangle .
sin π =
ππ
ππ
= π
π
sin ΞΈ β ΞΈ , sebab ΞΈ adalah kecil
ο π =
π
π
length of arc , x = Lο± (s = rο±)
ο± = π₯
πΏ
β΄
π
π
=
π₯
πΏ
π = π₯ (
π
πΏ
) for pendulum
f = xο·2 for SHM
14. 14
This shows that the oscillations of a simple pendulum is simple
harmonic.
ο·2 = π
πΏ
and ο· =
β(
π
πΏ
)
π =
2π
π
for SHM
β΄ π = β(
πΏ
π
) for pendulum
Periodic time and frequency of a simple pendulum is independent of
the mass of the pendulum and the angle oscillation (if this angle
exceeds 120) .
If ο· is the angular speed line generating SHM .
angular speed of the pendulum
ο = ο· ο(ο¦2
- ο±2
) and ο maximum = ο·ο¦
angular acceleration of the pendulum
ο‘ = ο·2
ο± and ο‘maximum = ο·2
ο¦
Periodic time , T = 2ο°ο
πππππ πππ πππππππππ‘
πππππ πππππππππ‘πππ
= 2ο° ο((
π
πΌ
)
15. 15
EXAMPLE 6
The amplitude of a simple pendulum is 7 0 and the periodic time is 5s ,
find:
i. maximum linear velocity of the pendulum weight and the
maximum angular speed of the pendulum cord ,
ii. maximum linear acceleration of the pendulum weight and
maximum angular acceleration of the pendulum cord .
EXAMPLE 7
A pendulum clock required rhythm second, with periodic time 2 s ,
was found late 80 s a day. The pendulum is shortened so that it
rhythm seconds exactly. Find the difference in the length of the
pendulum clock .
2.8 SIMPLE CONE
16. 16
figure shows a body B of mass M kg of rotate with ο· rad/s on the
vertical axis A-A and the angle ο± is assumed small. The forces acting
on the body is shown in the figure.
Tan ο± = Mrο·2 = rο·2
Mg g
But, tan ο± β π (Because π is too small)
ο ο± = rο·2
g
ο·
ο±
A
P
A
17. 17
And from space diagram,
Sin ο± = π
πΏ
ο± = π
πΏ
β΄ rο·2 = r and
π = β(
π
πΏ
)
g L
This is the minimum value of ο· for a conical pendulum , and the value
is equal to the value ο· for a simple pendulum and the pendulum is
in equilibrium.
From the force triangle
Tan ο± = Mrο·2
= rο·2
Mg g
From the space diagram
Tan ο± = r / h
β΄ rο·2
= r and ο· = ο(g/h)
g h
18. 18
Periodic time , T = 2π
π
for
β΄ π = 2πβ(
β
π
)
to get the tensile cord P, from triangle of forces,
sin ο± = πππ
π
2
and from spacediagram,
sin ο± = π
πΏ
β΄
π
πΏ
=
πππ
π
2
P = MLο·2 = πππΏ
β
EXAMPLE 8
Cord length a conical pendulum is 200 mm and weight is 2.4 kg. Find the rotation of the
pendulum at the moment leads to upward from its equilibrium position. If the cone
pendulum is rotating with a 88.8 rpm, determine:
i. Periodic time ,
ii. high-pendulum,
iii. the tension of the cord.
EXAMPLE 9
19. 19
Maximum permissible tension of the cord used for a conical pendulum
is 7 times heavier weight . If the cord length is 1.2 m , find:
i. angular speed in revolutions per minute ,
ii. high- pendulum,
iii. the change of high pendulum , when the angular speed dropped
to 20% .