realigns the suspending string with the new local

The formula shows that the period of a

gravity vector. Therefore, the angular motion of

simple pendulum is proportional to the square

the pendulum about the gravity vector for any

root of the length of the suspending string. The

horizontal acceleration of the suspension point is

longer the string, the longer the period.

zero. This particular pendulum is the *Schuler*

One property of the simple pendulum that is

very useful in the construction of an inertial

pendulum gets its name from the German

stable element is shown in figure 7-41. Two

engineer, Maximilian Schuler.

pendulums are suspended by strings of different

Schuler solved the problem of oscillating

lengths. Equal forces horizontally accelerate the

shipboard gyrocompasses in the early 1900s. Of

suspension point of each pendulum. The inertia

course, Schuler couldn't use the simple pendulum

of the bob resists the change in its state of

itself to solve this oscillating problem. He used

motion. This action causes the bob to lag the point

of suspension. It also produces an angular

the principle of the simple pendulum to construct

a pendulum that reacted like a simple pendulum.

motion of the pendulum about the local gravity

The length of this pendulum equals the radius of

vector. Figure 7-41 shows that the length of

the earth, which is about 3,440 nautical miles long.

pendulum (B) is longer than pendulum (A). It also

The period of oscillation for this pendulum is

shows angular motion of pendulum (B) is less than

about 84.4 minutes. Remember the period of

pendulum (A) for a corresponding linear motion

oscillation of a pendulum is proportional to the

of the suspension point. Therefore, the longer the

square root of its length. Therefore, any pen-

suspending string, the less the angular motion of

dulum constructed to oscillate with a period of

the pendulum for a given linear motion of the

84.4 minutes would have an equivalent length of

suspension point.

Consider what would happen in the following

about 3,440 nautical miles. Such a pendulum is

the Schuler pendulum, a special case of the

case. The suspending string is long enough to

compound or physical pendulum. Figure 7-42

maintain the bob at the center of the earth. The

shows three examples of compound pendulums.

suspension point is transported horizontally along

the earth's surface (fig. 7-40, view B). The bob

is hypothetically at the center of the earth, the seat

view A, the pivot point, P, is farthest away from

of the earth's gravity field. Accelerating the

the center of gravity, represented by distance d.

suspension point along the earth's surface merely