General physics


(system) #1

vibriation and waves

Simple harmonic motion= SHM

period=T

t=0

t= T\4=1\4 T

t= T\2= 1\2 T

t= 3T\4= 3\4 T

t=T

frequency=f
Number of oscillations per unit time

it is related by period(T) as follows

f=1\T

Unit of frequancy
1-
f=1\T=1\S= S

S= second
1-
SI UNIT ( SYSTEM INTERNATIONAL)= S

Unit of frequancy=hertz = HZ
Angular frequency= w

w= 2(3.14)\T

w= 2(3.14)f

Unit of angular frequency = rad/s

displaciment=X

Amplitude=A

Angular frequency= w
time = t

fain= phase angle

x(t)= A cos ( wt+fain
minimum value of cosine =1
maximum value of cosine = -1
Limit=+1 and -1

A and -A

Velocity = displacement \ time

Velocity of simple harmonic motion

displacement x(t)= A cos ( wt+ fain
velocity of SHM

d\dx cos x = - sin

d cos \ dt ( wt+fain) = - sin ( wt+ fain)*w

fain = phase constant

d\dx ( constant)=0

wA=Vmax

v(t)=dx\dt=d(Acos(wt+fain)\dt

= A-sin(wt+fain)*w

=wAsin(wt+fain

=Vmax sin(wt+fain

Acceleration of SHM = (a

d\dx=sinx=cosx
w2
w*w=w

wA=Vmax
w2
w A = a max

a(t)=dv\dt=d(-wAsin(wt+fain)\dt

wAcos(wt+fain)*w
w2
= w A cos (wt+fain -
= a max cos ( wt + fain -
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