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14. 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
15. Isme bhi 2 Type
displacement hoga
particle agar left side ka
distanct cover karega to
–ve displacement and
RHD + displacement.
16. Mean position se
extreme position
ke distance ko
amplidtude kehte
hai.
Isme bhi 2 type.
A+ and A-
22. 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.
37. 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.
60. S.H.M. As a Projection of U.C.M.
on any Diameter
S.H.M.
61. 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.
62. S.H.M. As a Projection of U.C.M. on any Diameter
A
O
B
C
D
At time t=0,
the particle P0
is at point D
P0
From ‘P0’ draw
a perpendicular
on diameter AB
M0
63. S.H.M. As a Projection of U.C.M. on any Diameter
A
O
B
C
D
P0
M0
Now if particle
performing
UCM
P1
M1
M2P2
64. S.H.M. As a Projection of U.C.M. on any Diameter
65. S.H.M. As a Projection of U.C.M. on any Diameter
69. 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
70. 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.
71. Let, in time ‘t’ the
particle reaches
point P
θ = ?
S.H.M. As a Projection of U.C.M. on any Diameter
72. S.H.M. As a Projection of U.C.M. on any Diameter
M
Expression for displacement(x)
x
73. S.H.M. As a Projection of U.C.M. on any Diameter
M
Expression for displacement(x)
x
74. S.H.M. As a Projection of U.C.M. on any Diameter
M
Expression for displacement(x)
x
75. S.H.M. As a Projection of U.C.M. on any Diameter
a = constant
76. S.H.M. As a Projection of U.C.M. on any Diameter
Oscillation ko samjhn se pehle hum different type ki moitoin ko samjht hai .
Zameeen ke nazdik agar koi motin hota hai jaise ke stone ka phekna stone curve banate hue kucch dori pe girjayga.
bhavra
Exception hai oscillation motion matlab wo motion jo repeat hota hai to and fro up and down like but periodic motion wo motin jo time based par repeat hota hai like mausam ka cycle. Isme waqt lagta hai repeat hone me lekin oscillation ek repeatative motion haie.
Yahan spring 2 high kheenchao kar rahi hai jise extreme position se dikhaya andar aur bahar. Point O wo position hai jahan spring ki dono extreme position ke beech ka hissa jahan wo dono side se equal hai ose mean position kaha hai. Wahan par spring ki force zero hoti hai. Nahi zyada nahi kum medium. Fark dekhe to zero hoga.
Wo jagah jaha spring ki khichaon sabse zyada hota hahi ose extreme positon kehte hai. Par hamare pass do extreme positon hai andar aur bahar. To dono ko kaise samjhe.
To hum agar ise Cartesian se samjhe matlab is ka graph me coordinate se samjhe to ek extreme point graph ke –ve and ek +ve ki taraf araha hai . That based oska naam hoga.
Jab mean postitin se spring +ve ki taraf badti hai to wo stretch hoti hai jis se osper ek opposite force lagta hai wo force jo mean position se aye distance ke opposite hota hai. Spring ke phelne se lagna wala force chahta hai ke spring dobara nazdik ajay dobara nazdic ane per wo comress hota hai again osper inertia lagta hai matlab chalete rehne wali body chalti rehti hai. Compress hone per mean positin se distance +ve hota lekin spring dobara phelne ke force distance ke opposite kaam karti hai . Jiski waja se force and distance hamesh ek dusre ke opposite rehte hahi.
First point ka mat;lab hai F equal hoti hai displacement ke . magnitude ka matlab haiForce ka directin kya hoga wo depend karta hai displacement and mean position per.
Yeh equation hame linear SHM ki malum ki hai. Newtwon ke second law ke mtabic force ka formula hai F=ma. Jisme accerlaration hai rate of change of velocity matlab change in velocity with time. Aur velocity ka formula hai distance per unit time.
F=ma me a ki value ai ose put kardo oske baad jo f ki value hai ose f= -Kx me put karo.
Yaha per hum k/m = constant ki jagaj w constant lenge is angular velocity w ke bare me hum age padhege. Abhi sirf samajh le.
Ab hum acceralration SHM ko samjhte hai yahan ek straight line hai jasper straight motion hora hai. Hame pata L = left extreme posoiton and R, O etc.ore ospe object motion kar raha hai. Jab koi particle motion perfume karta hai to oska displacement continuous change hota rehta hai. Jo ek postion pe rokta hai jise P bole jo ek particular time pe hua ho os time ko T se reperesent karege. Mean position se os particle p ka distance ko x suppose karege. Is distance ke zariye jum derive karege aceleratin, velocity aur displacement ko.
Jo system SHM perform karta hai osme extreme position me velocity zero hoti haih kyuni os position per momentum = mv. Yeh zero hojati hai.
Mean position pe distance zero hota hai jab yeh value velocity equation me rakhe to.
Alpha ke bare me hum baat me vistar me padhe ge.
Ab jum displacement base kuch cases dekhte hai os based per formula banate hai. Jab particle start hota hai mean postion se oski staritng t=0 aur x=0 hoga. X ki vlaue formula put karne per.
Yaha humlog samjhege jab koi object circle circular ghumta hai to andar ke point S.H.M oscillation karte hai.ise samjhte hai is circle se.
Circle pe ek point D hai jaha object Po ruka hai. Oswwaqt oski time and initial position is zero. Po perpendicular Mo hai. AB & CD diameter hai.
Circle pe ek point D hai jaha object Po ruka hai. Oswwaqt oski time and initial position is zero. Po perpendicular Mo hai. AB & CD diameter hai. Now dekhte hai ke jab particle circular motion me ghumta hai to line AB me kitna oscillation hota hai.
Yaha humlog samjhege jab koi object circle circular ghumta hai to andar ke point S.H.M oscillation karte hai.ise samjhte hai is circle se.
Yaha sin tita ka formula hai opposite / hypotanous.
Ab hum phase ke bare me padege ose hum displacement se understand karte hai. Hame phele se pata hai ke agar koi object D se start karta hao to P0 oska angle alpha hai aur thoda distance baat ka omega. In dono ko milane se hame total angle wt+ alpha milta hai. Per phase kya hai. Ose age samjhe ge.
Yahan per initial phase matlab starting phase se hone wale angle(magnitude) and direction change + or -. Phase shm ki definition hai displacement ka formula. To agar tiem zero ho tab shm alpha hoga. Jo means positon or initial stage me hi mumkin hai.
Yaha phase oski state of oscillation ko bata raha hai. A,v,x changes ko time based.
Time period hai one oscillation. Abhi mera object right R side me hai. Oswaqt time=0 hoga to yeh value formula put karne per kya alylga. To mean position se R tak distance x hai. Dekhte hai x ki
Length combination hai string aur bob ke radius ka total hai.