When Approximations Fail
PreLab Exercises
A mass of 0.250
±
0.001 kg is connected to the end of a light chord to make a pendulum.
The length between the pendulum’s axis of rotation and the mass is measured to be 0.800
±
0.005 m.
1.
Calculate the expected frequency of oscillation
࠵?
±
࠵?࠵?
for small angle oscillations
of the pendulum. Assume that g is exactly known to be 9.81
࠵?
/
࠵?
࠵?
.
Work:
࠵?
=
!
!
=
!
.
!"
.
!""
=
3
.
502
࠵?࠵?࠵?
/
࠵?
, angular frequency
!"
!"
=
!
!
!
!"
࠵?
×
࠵?
!
!
!
=
−
!
!
࠵?
!
!
!
࠵?
, angular frequency uncertainty
࠵?࠵?
=
−
1
2
࠵?
!
!
!
࠵?
0
.
005
!
=
±
0
.
011
Answer:
࠵?
=
3
.
502
±
0
.
011
࠵?࠵?࠵?
/
࠵?
2.
The angular position of a pendulum is measured using a Vernier rotary motion
sensor. The data collected are the opening angle of the pendulum– with respect to
vertical – measured in units of radians. The data are fit as shown in Figure 3.4.