3B SCIENTIFIC PHYSICS 1002956 Mode d'emploi - Page 4

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5. Example experiments
5.1 Free damped rotary oscillations
• To determine the logarithmic decrement Λ, the
amplitudes are measured and averaged out over
several runs. To do this the left and right deflec-
tions of the torsional pendulum are read off the
scale in two sequences of measurements.
• The starting point of the pendulum body is located
at +15 or –15 on the scale. Take the readings for
five deflections.
• From the ratio of the amplitudes we obtain Λ us-
ing the following equation
ϕ
n
Λ =
In
ϕ
n+1
ϕ
n
–
0 –15
–15
–15
–15
1 –14.8 –14.8 –14.8 –14.8 14.8 14.8 14.8 14.8
2 –14.4 –14.6 –14.4 –14.6 14.4 14.4 14.6 14.4
3 –14.2 –14.4 –14.0 –14.2 14.0 14.2 14.2 14.0
4 –13.8 –14.0 –13.6 –14.0 13.8 13.8 14.0 13.8
5 –13.6 –13.8 –13.4 –13.6 13.4 13.4 13.6 13.6
ϕ
n
Ø
–
Ø
0
–15
15
1
–14.8
14.8
2
–14.5
14.5
3
–14.2
14.1
4
–13.8
13.8
5
–13.6
13.5
• The average value for Λ comes to Λ = 0.0202.
• For the pendulum oscillation period T the follow-
ing is true: t = n · T. To measure this, record the
time for 10 oscillations using a stop watch and cal-
culate T.
T = 1.9 s
• From these values the damping constant δ can be
determined from δ = Λ / T.
δ = 0.0106 s
–1
• For the natural frequency ω the following holds
true
2
π
2
ω
=
 −
δ
2
T
ω = 3.307 Hz
5.2 Free damped rotary oscillations
• To determine the damping constant δ as a func-
tion of the current Ι flowing through the electro-
magnets the same experiment is conducted with
an eddy current brake connected at currents of
Ι = 0.2 A, 0.4 A and 0.6 A.
ϕ
+
15
15
15
15
ϕ
Λ –
Λ +
+
0.013
0.013
0.02
0.02
0.021
0.028
0.028
0.022
0.015
0.022
Ι Ι Ι Ι Ι = 0.2 A
ϕ
n
–
0 –15
–15
–15
1 –13.6 –13.8 –13.8 –13.6 –13.7
2 –12.6 –12.8 –12.6 –12.4 –12.6
3 –11.4 –11.8 –11.6 –11.4 –11.5
4 –10.4 –10.6 –10.4 –10.4 –10.5
5
9.2
–9.6
• For T = 1.9 s and the average value of Λ = 0.1006
we obtain the damping constant: δ = 0.053 s
Ι Ι Ι Ι Ι = 0.4 A
ϕ
n
0
–15
–15
–15
1
–11.8 –11.8
–11.6 –11.6
2
–9.2
–9.0
3
–7.2
–7.2
4
–5.8
–5.6
5
–4.2
–4.2
• For T = 1.9 s and an average value of Λ = 0.257 we
obtain the damping constant: δ = 0.135 s
Ι Ι Ι Ι Ι = 0.6 A
ϕ
n
0
–15
–15
–15
1
–9.2
–9.4
2
–5.4
–5.2
3
–3.2
–3.2
4
–1.6
–1.8
5
–0.8
–0.8
• For T = 1.9 s and an average value of Λ = 0.5858
we obtain the damping constant: δ = 0.308 s
5.3 Forced rotary oscillation
• Take a reading of the maximum deflection of the
pendulum body to determine the oscillation am-
plitude as a function of the exciter frequency or
the supply voltage.
T = 1.9 s
Motor voltage V
3
4
5
6
7
7.6
8
9
10
9
ϕ
Λ –
Ø
–
–15
–15
0.0906
0.13
0.0913
0.0909
–9.6
–9.6
–9.5
0.1
ϕ
Λ –
–
Ø
–
–15
–15
–11.7
0.248
–9.0
–9.2
–9.1
0.25
–7.0
–7.0
–7.1
0.248
–5.4
–5.2
–5.5
0.25
–4.0
–4.0
–4.1
0.29
–1
ϕ
Λ –
–
Ø
–
–15
–15
–9.2
–9.2
–9.3
0.478
–5.6
–5.8
–5.5
0.525
–3.2
–3.4
–3.3
0.51
–1.8
–1.8
–1.8
0.606
–0.8
–0.8
–0.8
0.81
ϕ
0.8
1.1
1.2
1.6
3.3
20.0
16.8
1.6
1.1
–1
–1