Section 14 1 .
SHI is motion in which the net force is proportional
simple harmonic motion acting on object
·
to opposite direction of displacement from equilibrium.
X(t) =
Asin wt +
Oo
if we are given initial positions usually X(O)
,
and v O
,
then we find A, 0
.
Ex .
14 1 . Section 14 . 2
1 = 56 . 0 Im ·
simple pendulum is a mass (bob) at end of a massless
m= 1 00 string
.
kg .
(0) 0 055m here , the force-mgsino restoring force
+
x = . acts as a
v(0) Following same logic find
·
= -
3 2 m/s
. we
2
9 Sing
-
=
w = = =
7 48
.
rads
X (0) : Asin O. As long as O is less than about 0 5 rad
. 300 ,
we can
+
0 055 = AsinO, use small which says that sino 0
.
angle approximation ,
=
= C = -
70
v (t) =
Awcos wt + 00 compare to a:x
v(O) =
Awcos O
·
3 2
.
= Aw cos D
·
O(t) Asin (wt = + o)
0
this time ,
w =
9
3 2= AWCOSO , And thus
2-
T
- ·
.
=
,
+ 0 055. : AsinO ,
Ex
-
3 2 .
=
WootO . T =
2n
-g
0 055
= Eg
.
- : 1 4800
.
= Eg
Oo =
2 234 rad
.
A
=
0 070m
= .
9
g 4π (0 75)
=
if
spring is hanging vertically, .
(1 7357)2
.
we can treat system in same way ; the
9 8281 M/sz
effect of gravity is to
change the equilibrium g =
.
position .
SHI is motion in which the net force is proportional
simple harmonic motion acting on object
·
to opposite direction of displacement from equilibrium.
X(t) =
Asin wt +
Oo
if we are given initial positions usually X(O)
,
and v O
,
then we find A, 0
.
Ex .
14 1 . Section 14 . 2
1 = 56 . 0 Im ·
simple pendulum is a mass (bob) at end of a massless
m= 1 00 string
.
kg .
(0) 0 055m here , the force-mgsino restoring force
+
x = . acts as a
v(0) Following same logic find
·
= -
3 2 m/s
. we
2
9 Sing
-
=
w = = =
7 48
.
rads
X (0) : Asin O. As long as O is less than about 0 5 rad
. 300 ,
we can
+
0 055 = AsinO, use small which says that sino 0
.
angle approximation ,
=
= C = -
70
v (t) =
Awcos wt + 00 compare to a:x
v(O) =
Awcos O
·
3 2
.
= Aw cos D
·
O(t) Asin (wt = + o)
0
this time ,
w =
9
3 2= AWCOSO , And thus
2-
T
- ·
.
=
,
+ 0 055. : AsinO ,
Ex
-
3 2 .
=
WootO . T =
2n
-g
0 055
= Eg
.
- : 1 4800
.
= Eg
Oo =
2 234 rad
.
A
=
0 070m
= .
9
g 4π (0 75)
=
if
spring is hanging vertically, .
(1 7357)2
.
we can treat system in same way ; the
9 8281 M/sz
effect of gravity is to
change the equilibrium g =
.
position .
