To Oscillations
47
Simple harmonic motion and oscillations
Oscillations
-
lerms
Periodic motion-motion that repeats itself at
regular time interval
Oscillation -
Back and fourth motion
periodic
Types of oscillations
Free
Object can vibrate on its own without application of continues external F
2 g
.
. Pendulum with no friction
Dampenen
Damping forces slow dow escillations this
making them loose energy
e g
.
.
Pendulum with friction
Forced
External force acts to keep oscillation in regular time intervals
e .
.
g Shing with friction and someone
pushing them IF casel out
Forces and simple harmonic motion SHM
Terms
Simple harmonic motion -
Motion
occurring when a linear restoring force is exerted on an object
displaced from
equilibrium position
Restoring force -
Force that always acts towards the equilibrium posisition in an oscillation
Equilibrium position -
The position where there is no restoring force acting on an oscillating
Object and the net force is Zero
Example : Block attached to
spring on frictionlessSurface (free) compressed Xo
-
Equilibrium
Object will accelerate to
equilibrium posisition after block is displaced Related posisition
Force must cause acceleration (neuton #)(Restoring ferce Stretched F :
Restoring force
E F
+
x = -
1 x = g x =
1
Fr = Espring = Fr Espring = Fr
& &
&
=
=
Fg Fg
=
Fg
Hookes law
External/Applied force
F =
Ke
spring
Restoring force
Espring = -Kes
Where
:
Displacement
K
Spring constant (N m')
: .
measure of stiffness of
spring
If
spring is stretched
Direction of Stretch is+ direction
↑
Espring +kes
If
spring is compressed
Direction of compressed is -
direction
Espring =
kes
-
-
Newton
Fnet
#
=
and
ma
SHM
#
Espring :
Ma T= I
=
where F
Spring is
only Force f =
T
kx
fi
=
ma
-
a = W'r /From centripula motion)
a = -
Wax (W : Angula frequency Only valid for frictionless ocillation
-
kx = -
Wom
mW" =
4 el
&= Centriper motion
oly for horizontal
8 block no friction
, Free : No external forces to
allowing is continue foreve
1
Forced : External force that balances other forces allowing it to continue forens
Yes ,
forced-
Yes forced free
,
Yes ,
camperen No escilation
Yes ,
demponen
~
Periodic it 1
,
as
only occurs in direction
Espring Kes
k(k 2)
-
10 , 0 =
0 =
1
,
-
~
1
= 6 6)
,
10' N .
M
1, 2 + 10 "N . "
m "I will halve
No e must be small
compared to mat
stress/compression
Otherwise
spring will break
Espring =
Kos
-
10 35 +
,
103 = (2 , 8 = p3)xs -
+
for
for
compression
stretch
x =
3,7m ~
47
Simple harmonic motion and oscillations
Oscillations
-
lerms
Periodic motion-motion that repeats itself at
regular time interval
Oscillation -
Back and fourth motion
periodic
Types of oscillations
Free
Object can vibrate on its own without application of continues external F
2 g
.
. Pendulum with no friction
Dampenen
Damping forces slow dow escillations this
making them loose energy
e g
.
.
Pendulum with friction
Forced
External force acts to keep oscillation in regular time intervals
e .
.
g Shing with friction and someone
pushing them IF casel out
Forces and simple harmonic motion SHM
Terms
Simple harmonic motion -
Motion
occurring when a linear restoring force is exerted on an object
displaced from
equilibrium position
Restoring force -
Force that always acts towards the equilibrium posisition in an oscillation
Equilibrium position -
The position where there is no restoring force acting on an oscillating
Object and the net force is Zero
Example : Block attached to
spring on frictionlessSurface (free) compressed Xo
-
Equilibrium
Object will accelerate to
equilibrium posisition after block is displaced Related posisition
Force must cause acceleration (neuton #)(Restoring ferce Stretched F :
Restoring force
E F
+
x = -
1 x = g x =
1
Fr = Espring = Fr Espring = Fr
& &
&
=
=
Fg Fg
=
Fg
Hookes law
External/Applied force
F =
Ke
spring
Restoring force
Espring = -Kes
Where
:
Displacement
K
Spring constant (N m')
: .
measure of stiffness of
spring
If
spring is stretched
Direction of Stretch is+ direction
↑
Espring +kes
If
spring is compressed
Direction of compressed is -
direction
Espring =
kes
-
-
Newton
Fnet
#
=
and
ma
SHM
#
Espring :
Ma T= I
=
where F
Spring is
only Force f =
T
kx
fi
=
ma
-
a = W'r /From centripula motion)
a = -
Wax (W : Angula frequency Only valid for frictionless ocillation
-
kx = -
Wom
mW" =
4 el
&= Centriper motion
oly for horizontal
8 block no friction
, Free : No external forces to
allowing is continue foreve
1
Forced : External force that balances other forces allowing it to continue forens
Yes ,
forced-
Yes forced free
,
Yes ,
camperen No escilation
Yes ,
demponen
~
Periodic it 1
,
as
only occurs in direction
Espring Kes
k(k 2)
-
10 , 0 =
0 =
1
,
-
~
1
= 6 6)
,
10' N .
M
1, 2 + 10 "N . "
m "I will halve
No e must be small
compared to mat
stress/compression
Otherwise
spring will break
Espring =
Kos
-
10 35 +
,
103 = (2 , 8 = p3)xs -
+
for
for
compression
stretch
x =
3,7m ~
