3B Scientific Pohl's Torsion Pendulum User Manual

Page 9

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

Λ =













n+1

–

0 –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

–

Λ –

Λ +

–15

–14.8

14.8

0.013

–14.5

14.5

0.02

–14.2

14.1

0.021

0.028

–13.8

13.8

0.028

0.022

–13.6

13.5

0.015

0.022

• 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

= 






−

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.

ΙΙΙΙΙ = 0.2 A

–

Λ –

0 –15

–15

1 –13.6

–13.8

–13.6 –13.7

0.0906

2 –12.6

–12.8

–12.6

–12.4 –12.6

0.13

3 –11.4

–11.8

–11.6

–11.4 –11.5

0.0913

4 –10.4

–10.6

–10.4

–10.4 –10.5

0.0909

5 9.2

–9.6

–9.6 –9.5

0.1

• For T = 1.9 s and the average value of Λ = 0.1006

we obtain the damping constant:

δ = 0.053 s

–1

ΙΙΙΙΙ = 0.4 A

–

Λ –

–15

–11.8 –11.8

–11.6

–11.7

0.248

–9.2 –9.0

–9.0

–9.2

–9.1

0.25

–7.2 –7.2

–7.0

–7.1

0.248

–5.8 –5.6

–5.4

–5.2

–5.5

0.25

–4.2 –4.2

–4.0

–4.1

0.29

• For T = 1.9 s and an average value of Λ = 0.257 we

obtain the damping constant:

δ = 0.135 s

–1

ΙΙΙΙΙ = 0.6 A

–

Λ –

–15

–9.2

–9.4

–9.2 –9.2

–9.3

0.478

–5.4

–5.2

–5.6 –5.8

–5.5

0.525

–3.2

–3.2 –3.4

–3.3

0.51

–1.6

–1.8

–1.8 –1.8

–1.8

0.606

–0.8

–0.8 –0.8

–0.8

0.81

• For T = 1.9 s and an average value of Λ = 0.5858

we obtain the damping constant:

δ = 0.308 s

–1

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

0.8

1.1

1.2

1.6

3.3

7.6

20.0

16.8

1.6

1.1