A simple method for the determination of qPlus sensor spring constants

John Melcher1, Julian Stirling1, Gordon A Shaw1

  • 1National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.

Related Concept Videos

Euler's Formula to Columns: Problem Solving01:23

Euler's Formula to Columns: Problem Solving

Euler's formula is used in structural engineering to determine the buckling load of columns under various conditions. However, when dealing with systems that incorporate both rigid elements and elastic components, such as springs, the analysis requires a finer approach to determine the critical load. The problem described involves two rigid bars connected at a pivot point with a spring attached and a vertical load applied at one end.
The system comprises two vertical rigid bars, AB and BC, of...
1.1K
Thermal expansion and Thermal stress: Problem Solving01:27

Thermal expansion and Thermal stress: Problem Solving

San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55...
2.4K
Generalized Hooke's Law01:22

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
3.2K
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
1.6K
Frequency of Spring-Mass System01:17

Frequency of Spring-Mass System

One interesting characteristic of the simple harmonic motion (SHM) of an object attached to a spring is that the angular frequency, and the period and frequency of the motion, depend only on the mass and the force constant of the spring, and not on other factors such as the amplitude of the motion or initial conditions. We can use the equations of motion and Newton's second law to find the angular frequency, frequency, and period.
Consider a block on a spring on a frictionless surface. There...
8.3K
Substitution Rule Applied to Indefinite Integrals01:27

Substitution Rule Applied to Indefinite Integrals

When a force is applied to a linear spring, the restoring force increases proportionally with the amount of displacement. This behavior is described by Hooke’s law, which allows the work done on the spring to be determined directly from the force–displacement relationship. In this case, the force varies in a simple and predictable manner, making the calculation relatively simple.On the other hand, a nonlinear spring does not obey Hooke’s law. Its restoring force depends on...
194