Spring
The zeroAength springgravity meter
By LUCIEN LaCOSTE Austin, Texas
took my only formal geophysics coursein 1932at the University of Texas. Arnold Romberg was the teacher. Early in the course,he explained the .theory of the horizontal pendulum and showed that theoretically it has an infinite period when its axis of rotation is vertical. It behaves like a sphere on a perfectly horizontal table - i.e., the sphere stays wherever it is put. Romberg also told us that no verticalseismographhad ever been designed with equally good characteristics. A few days later he sent his entire class to the blackboard, each with a different problem. Mine was to design a new type of vertical seismograph. I gave it my best efforts but found nothing new. However, the problem was interesting and I kept thinking about it. I am an incurable optimist, so I began looking in earnest for a theoretically infinite period in a vertical seismograph just because the horizontal pendulum had one. I started with the simple suspension shown in Figure 2 of the original article which follows this foreword. There are two torques, gravitational and spring, in this system. The condition that will produce an infinite period is that the two torques balance each other exactly for any angle 0. Since the gravitational torque varies as sin 0, the spring torque must also. However, the spring torque is the product of two variables, the pull of the spring and the lever arm. Can we expresssin 8 as a product of two trigonometric functions? Yes,sin 0 = 2 sin 8/2 cos 8/2. Next, can we show that a! = /3 = 0/2? Since we have postulated that the fixed and movable arms of the suspension be equal, Q = /3. A geometry theorem states that 0 is measured by the arc FE which means that CY, which is measured by half the same arc, equals 8/2.
I
An inspection of Figure 2 shows that the first condition is met, but the second condition is fulfilled only if the force exerted by the spring is proportional to its length. In other
By LUCIEN LaCOSTE Austin, Texas
took my only formal geophysics coursein 1932at the University of Texas. Arnold Romberg was the teacher. Early in the course,he explained the .theory of the horizontal pendulum and showed that theoretically it has an infinite period when its axis of rotation is vertical. It behaves like a sphere on a perfectly horizontal table - i.e., the sphere stays wherever it is put. Romberg also told us that no verticalseismographhad ever been designed with equally good characteristics. A few days later he sent his entire class to the blackboard, each with a different problem. Mine was to design a new type of vertical seismograph. I gave it my best efforts but found nothing new. However, the problem was interesting and I kept thinking about it. I am an incurable optimist, so I began looking in earnest for a theoretically infinite period in a vertical seismograph just because the horizontal pendulum had one. I started with the simple suspension shown in Figure 2 of the original article which follows this foreword. There are two torques, gravitational and spring, in this system. The condition that will produce an infinite period is that the two torques balance each other exactly for any angle 0. Since the gravitational torque varies as sin 0, the spring torque must also. However, the spring torque is the product of two variables, the pull of the spring and the lever arm. Can we expresssin 8 as a product of two trigonometric functions? Yes,sin 0 = 2 sin 8/2 cos 8/2. Next, can we show that a! = /3 = 0/2? Since we have postulated that the fixed and movable arms of the suspension be equal, Q = /3. A geometry theorem states that 0 is measured by the arc FE which means that CY, which is measured by half the same arc, equals 8/2.
I
An inspection of Figure 2 shows that the first condition is met, but the second condition is fulfilled only if the force exerted by the spring is proportional to its length. In other