PASCO ME-9833 Physical Pendulum Set - Manual (Page 26)

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Model No. ME-9833 Physical Pendulum Set
26
3. How do you know that the center hole is the center of gravity?
Answers will vary. One way to confirm that the center hole is the center of gravity is to balance the
irregular shape on a fingertip.
Sample Data for Experiment 2: Minimum Period of an Oscillating Bar
The screenshot shows typical data for the length from the pivot point to the center of gravity of an
oscillating pendulum bar and the corresponding period of oscillation for each length.
Calculations
Derivation of the length for minimum period, . Find the derivative of the expression for
the period of oscillation, T.
Set the derivative equal to zero and solve for L
cg
. For example,
L
cg
1
12
----------L =
T 2 π
1
12
------ML
2
ML
cg
2
+
MgL
cg
------------------------------------------- =
dT
dL
cg
------------ π
1
12
------L
2
L
cg
2
+
gL
cg
-------------------------------
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
1
2
--- –
g
1
12
------L
2
L
cg
2
+
⎝ ⎠
⎛ ⎞ gL
cg
2L
cg
( ) –
gL
cg
( ) 2
--------------------------------------------------------------------------- × =
dT
dL
cg
------------ π
1
12
------L
2
L
cg
2
+
gL
cg
-------------------------------
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
1
2
--- – 1
12
------L
2
L
cg
2
+
⎝ ⎠
⎛ ⎞
2L
cg
( )
2
–
g L
cg
( ( ) 2
-------------------------------------------------------------- Ч =