Summary Further Studies Physics IEB/ISC Topic 6 Oscillations

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 ~