Forced vibrations & resonance
Periodic motion :
Simple Harmonic Systems those
:
which oscillate
:
With SHM
vibrations occur when no ex
CircularMotion :
force is continuosly the
sys
Examples :
Simple Pendulum acting on
object moving in Circular
path at Constant
from
↳ objects will oscillate at na
speed >
-
Constantly Changing velocity
mass
,
M
hangs string of
3. accelerating length ,
1 Mass is
displaced by small
Forced
(entripetal
.
:
acceleration, vibrations -
angle
les than & when let will oscillate system e
go
T
↳ Newton -
1.
war
1 -
must have
eresultant force
a = = external
drivi
then f
↓ using am
=
↳ causes it
Acts toward Centre
velocityf of circle /CENTRIPETAL FORCE
f-mmG as then
approximation ↳ if
-
is valid
frequency of driv
⑭
speed (c) angle an object frequency)
2
natu
Angular
=
centripetal
Mass-Spring System T
=
-
> =
&
force moves
through per
I
N
unit time
spring
2
types horizontal
I
spring is
-
>
↓ Objects linear speed constant
J
Y=
radians
W ↳ KE
zif
astof or vertical is converted
-
-
to ELASTIC
I
↑
radius
of circular
KE is converted to
path travelling Further Mechanics
&
in both ELASTIC
Radians the sector of when the arc of that sector GRAVITATIONAL
angle in a circle
length
:
is
equal to the radius of the circle
.
°
360 = 24 radians
D R Xπ
aaphs
= : :
To
R -
D
displacement time graph
:
u Acos Lot
x
= >
-
At centre of oscillations >
-
KE
-
A
G
x
I ↳ as moves away
displacement system
force Aforce that restores equilibrium KE-GP
Restoring
=
>
-
nation
Periodic motion :
Simple Harmonic Systems those
:
which oscillate
:
With SHM
vibrations occur when no ex
CircularMotion :
force is continuosly the
sys
Examples :
Simple Pendulum acting on
object moving in Circular
path at Constant
from
↳ objects will oscillate at na
speed >
-
Constantly Changing velocity
mass
,
M
hangs string of
3. accelerating length ,
1 Mass is
displaced by small
Forced
(entripetal
.
:
acceleration, vibrations -
angle
les than & when let will oscillate system e
go
T
↳ Newton -
1.
war
1 -
must have
eresultant force
a = = external
drivi
then f
↓ using am
=
↳ causes it
Acts toward Centre
velocityf of circle /CENTRIPETAL FORCE
f-mmG as then
approximation ↳ if
-
is valid
frequency of driv
⑭
speed (c) angle an object frequency)
2
natu
Angular
=
centripetal
Mass-Spring System T
=
-
> =
&
force moves
through per
I
N
unit time
spring
2
types horizontal
I
spring is
-
>
↓ Objects linear speed constant
J
Y=
radians
W ↳ KE
zif
astof or vertical is converted
-
-
to ELASTIC
I
↑
radius
of circular
KE is converted to
path travelling Further Mechanics
&
in both ELASTIC
Radians the sector of when the arc of that sector GRAVITATIONAL
angle in a circle
length
:
is
equal to the radius of the circle
.
°
360 = 24 radians
D R Xπ
aaphs
= : :
To
R -
D
displacement time graph
:
u Acos Lot
x
= >
-
At centre of oscillations >
-
KE
-
A
G
x
I ↳ as moves away
displacement system
force Aforce that restores equilibrium KE-GP
Restoring
=
>
-
nation
