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 -
شكرا الكم خلصت المحاضرة اليوم