Page 188 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 14] SIMPLE HARMONIC MOTION 173

SOLVED PROBLEM 14.13
(a) A pendulum clock is in an elevator that descends at a constant velocity. Does it keep correct time?
(b) The same clock is in an elevator in free fall. Does it keep correct time?
(a) The motion of the pendulum bob is not affected by motion of its support at constant velocity, so the clock keeps
correct time.
(b) In free fall the pendulum’s support has the same downward acceleration of g as the bob, so no oscillations occur
and the clock does not operate at all.

SOLVED PROBLEM 14.14
A lamp is suspended from a high ceiling with a cord 12 ft long. Find its period of oscillation.

L 12 ft
T = 2π = 2π = 3.85 s
g 32 ft/s 2
SOLVED PROBLEM 14.15

Find the length in meters of a simple pendulum whose period is 2 s.
√
The first step is to solve the formula T = 2π L/g for L. We proceed as follows:
2
4π L
2
T =
g
gT 2
L =
4π 2
2
Now we substitute g = 9.8 m/s and T = 2 s, and we obtain
2
(9.8 m/s )(2s) 2
L = = 0.993 m
4π 2
SOLVED PROBLEM 14.16
A broomstick 1.5 m long is suspended from one end and set in oscillation. (a) What is the period of
1
2
oscillation? (The moment of inertia of a thin rod pivoted at one end is I = mL .) (b) What would be
3
the length of a simple pendulum with the same period?
(a) The distance h from the pivot to the center of gravity of the broomstick is L/2. Hence

2
I mL /3 2L (2)(1.5m)
T = 2π = 2π = 2π = 2π = 2.01 s
2
mgh mgL/2 3g (3)(9.8 m/s )
(b) From the solution to Prob. 14.15,
2
gT 2 (9.8 m/s )(2.01 s) 2
L = = = 1.0m
4π 2 4π 2
SOLVED PROBLEM 14.17
A certain torsion pendulum consists of a 2-kg horizontal aluminum disk 15 cm in radius that is suspended
from its center by a wire. When a torque of 1 N·m is applied to the disk, it rotates through 15 . Find the
◦
frequency of oscillation of the disk.
Since 1 = 0.01745 rad, 15 = 0.262 rad, and the torque constant of the suspension wire is
◦
◦
τ 1N·m
K = = = 3.82 N·m/rad
θ 0.262 rad