Oscillation

Tuning

fork

Spring of

mass

Are oscillatory

motion is

periodic

motion?

Terminologies of Oscillatory

motion

E M E

Extreme

position

Mean

position

O

Extreme

position

Extreme

position

Mean

position

O

Extreme

positionE M E

Extreme

position

Mean

position

O

Extreme

position

AGAR ISE CARTESIAN SE

UNDERSTAND KARE TO EK

EXTREME POINT + AND –VE.

- +

P called left

extreme or –ve

extreme.

R called right

exteme or + ve

extreme.

R

Isme bhi 2 Type

displacement hoga

particle agar left side ka

distanct cover karega to

–ve displacement and

RHD + displacement.

Mean position se

extreme position

ke distance ko

amplidtude kehte

hai.

Isme bhi 2 type.

A+ and A-

Ek extreme se

dusre extreme ka

distance range or

path length hai.

One osclllation = mean positin se start and

cover right extreme then left exteme then

again come mean position.

Harmonic motion

Harmonic motion

Koi bhi spring jab

movement karta hai to

oske displacement,

velocitiy and

acceleration me time ke

based continuous

changes ata hai jise

graph se show kiya hai.

Jise meths ke zarie

show karte hai.

Simple Harmonic Motion

SHM me 2 type hai linear

and angular.

Linear means straight

motion and angular mean

making angle motion.

Linear simple Harmonic motion

F

Now remaining concept is

same because again

distance and force are in

opposite directin so same

forumula

F = -kx

Definition of linear SHM

F= restoring force.

Aise motion linear

nahi hosakte kynki

inka distance depend

hota rehta hai gravity

ki waha se.

Differential Equation of the linear S.H.M

F = ma

But Acc. to

newton second

law Force

formula is

F=ma.But Acceleration is a = dv/dt

Velocity is v = dx/dt

Now put v ka value

in acceleration

forumula dv me.

Substituting equation (iii) in equation

(i)Divide

by m

Expression for Acceleration

in linear S.H.M

Left extreme

position

Right extreme

positionMean

position

PX

a = ?

V = ?

x = ?

Straight line me

object motion karte

ek point P per rukta

hai. Jiska distance x

& time t.

With help of x we

can fine

acceleration,

velocity and

distance.

We already found

a = d2x/dt2

- Sign indicate

acceleration and

displacement are in

opposite direction.

We know angular

velocity is const.

then…

Kya ho agar particle

mean position pe ho.

To displacement zero

hoga.

Expression for Velocity in

Linear S.H.M

Multiply and divide by dx

Separating the

variable

Where ‘c’ constant of integration.

By square root

both side

Expression for Maximum

and Minimum velocity

Expression for Displacement

in Linear S.H.M

Taking sin both

side,

S.H.M. As a Projection of U.C.M.

on any Diameter

S.H.M.

S.H.M. As a Projection of U.C.M. on any Diameter

A O B

C

D

Let AB and CD be

the diameter of the

circle and ‘O’ be

the Centre of the

circle.

S.H.M. As a Projection of U.C.M. on any Diameter

AO

B

C

D

At time t=0,

the particle P0

is at point D

P0

From ‘P0’ draw

a perpendicular

on diameter AB

M0

S.H.M. As a Projection of U.C.M. on any Diameter

AO

B

C

DP0

M0

Now if particle

performing

UCM

P1

M1

M2P2

S.H.M. As a Projection of U.C.M. on any Diameter

S.H.M. As a Projection of U.C.M. on any Diameter

A OB

C

DA O B

A OB

C

DA O B

Derivation of S.H.M as a projection

of U.C.M on any diameter

S.H.M. As a Projection of U.C.M. on any Diameter

A O B

C

D

Consider, a particle

performing U.C.M

with an angular

velocity ω along a

circle of radius ‘a’.

a

ω

S.H.M. As a Projection of U.C.M. on any Diameter

Suppose the

particle start from

position Po.

α

‘α’ is the initial

phase angle or

epoch.

Let, in time ‘t’ the

particle reaches

point P

θ = ?

S.H.M. As a Projection of U.C.M. on any Diameter

S.H.M. As a Projection of U.C.M. on any Diameter

M

Expression for displacement(x)

x

S.H.M. As a Projection of U.C.M. on any Diameter

M

Expression for displacement(x)

x

S.H.M. As a Projection of U.C.M. on any Diameter

M

Expression for displacement(x)

x

S.H.M. As a Projection of U.C.M. on any Diameter

a = constant

S.H.M. As a Projection of U.C.M. on any Diameter

M

Phase of S.H.M 1

Magnitude matlab angle

, distance, a, v ka

measure asani se

karsakte hai. Aur saath

saath direction pata

karsakte hai motion

kidhar horaha hai.

Agar mujhe angle pata ho to me

easily x ki value find kar sakta

hoo.

If angle is 0 degree

iska matlab

displacement

particle mean

postion se start ho

rahe hai.

OB wala particle zero se start

hua hai. Isliye angle 0. and DB

wala object distance cover

karke 90 degree angle bana

raha hai.

Magnitude means

oscillation ki state

bataye mean a,v,t,x

etc.

INITIAL PHASE (EPOCH) OF S.H.M.

YEH wo phase hai jaha per

particle apni initial stage per

hai abhi movement start nahi

ki isliye angle 0 means mean

postion.

Expression fro time period and

frequency in linear S.H.M

x

Hamara

particle R

side hai.

Graphical Representation of

S.H.M- Mean position-1

A

0

0 -A 0

0

Introduction to Simple pendulum

Simple pedulam me ek

heavy mass jise bob kehte

hai. String jisse bob tigh

kiya hai.

Pendulam ki length bob se

rigid ka distance hai.

Motion of Simple Pendulam as

S.H.M.

If pendulum is

displaced through a

angle θ

Motion of Simple Pendulum as a S.H.M.

mg

x

Expression for time period

Laws of simple pendulum

Second pendulum

If π =constant.

Damped Force

NO

Why?

Differential equation of Damped

Harmonic Oscillations

Displacement equation of dumped

harmonic oscillation