spring constant

(noun)

a characteristic of a spring which is defined as the ratio of the force affecting the spring to the displacement caused by it

Related Terms

Examples of spring constant in the following topics:

  • Energy in a Simple Harmonic Oscillator

    • where PE is the potential energy, k is the spring constant, and x is the magnitude of the displacement or deformation.
    • For example, for a simple pendulum we replace the velocity with v=Lω, the spring constant with k=mg/L, and the displacement term with x=Lθ.
    • A known mass is hung from a spring of known spring constant and allowed to oscillate.
    • This value is compared to a predicted value, based on the mass and spring constant.
    • Explain why the total energy of the harmonic oscillator is constant

  • Hooke's Law

    • For instance, the spring is pulled downwards with either no load, Fp, or twice Fp.
    • k is a constant called the rate or spring constant (in SI units: N/m or kg/s2).
    • It's possible for multiple springs to act on the same point.
    • The slope of this line corresponds to the spring constant k.
    • The extension of the spring is linearly proportional to the force.

  • Simple harmonic oscillation

    • The constant of proportionality is called the spring constant and is usually denoted by k.
    • First compute the spring constant of the spring using the data above.
    • You'll see that with or without the added 60 g mass, the spring constant is about 25 N/m.
    • Now consider the "spring constant" of a diatomic molecule.
    • What you will find is that the spring constant is within a factor of 2 or 3 the same as the spring we used in class!

  • The energy method

    • And the potential energy of a spring is the spring constant times the square of amount the spring is compresses or extended.
    • The energy approach is easily extended to an arbitrary number of springs and masses.
    • For now we will assume that we have $n$ springs, the end springs being connected to rigid walls, and $n-1$ masses.
    • So, $n-1$ masses $\{m_i\}_{i=1,n-1}$ and $n$ spring constants $\{k_i\}_{i=1,n}$ .
    • For now, let's simplify Equation 1.2.33 by taking all the masses to be the same $m$ and all the spring constants to be the same $k$ .

  • Springs

    • Spring force is conservative force, given by the Hooke's law : F = -kx, where k is spring constant, measured experimentally for a particular spring and x is the displacement .
    • We would like to obtain an expression for the work done to the spring.
    • The displacement x is usually measured from the position of "neutral length" or "relaxed length" - the length of spring corresponding to situation when spring is neither stretched nor compressed.
    • When we stretch the spring.
    • Neglecting frictional forces, Mechanical energy conservation demands that, at any point during its motion,$\begin{aligned} Total ~Energy &= \frac{1}{2} m v^2 + \frac{1}{2}k x^2 \\ &= \frac{1}{2} k x_f^2 = constant.

  • Period of a Mass on a Spring

    • The period of a mass m on a spring of spring constant k can be calculated as $T=2\pi \sqrt{\frac{m}{k}}$.
    • The mass and the force constant are both given.
    • Here, F is the restoring force, x is the displacement from equilibrium or deformation, and k is a constant related to the difficulty in deforming the system (often called the spring constant or force constant).
    • A typical physics laboratory exercise is to measure restoring forces created by springs, determine if they follow Hooke's law, and calculate their force constants if they do .
    • The stiffer the spring is, the smaller the period T.

  • Forced motion

    • To model it we need to add another term to the equation of motion of the spring/mass.
    • In the first place the spring would stretch to the point of breaking; but also, dissipation, which we have neglected, would come into play.
    • Figure 1.2: A linear spring satisfies Hooke's law: the force applied by the spring to a mass is proportional to the displacement of the mass from its equilibrium, with the proportionality being the spring constant.
    • Since the spring wants to return to its equilibrium, the force must have the opposite sign as the displacement.

  • Work

    • If $F$ is constant, in addition to being directed along the line, then the integral simplifies further to:
    • This calculation can be generalized for a constant force that is not directed along the line, followed by the particle.
    • Let's consider an object with mass $m$ attached to an ideal spring with spring constant $k$.
    • When the object moves from $x=x_0$ to $x=0$, work done by the spring would be:
    • The spring applies a restoring force ($-k \cdot x$) on the object located at $x$.

  • Simple Harmonic Motion

    • It can serve as a mathematical model of a variety of motions, such as the oscillation of a spring.
    • where m is the mass of the oscillating body, x is its displacement from the equilibrium position, and k is the spring constant.
    • In the solution, c1 and c2 are two constants determined by the initial conditions, and the origin is set to be the equilibrium position.
    • Each of these constants carries a physical meaning of the motion: A is the amplitude (maximum displacement from the equilibrium position), ω = 2πf is the angular frequency, and φ is the phase.
    • Graphs of x(t),v(t), and a(t) versus t for the motion of an object on a spring.

  • Work Done by a Variable Force

    • The work done by a constant force of magnitude F on a point that moves a displacement $\Delta x$ in the direction of the force is simply the product
    • For example, let's consider work done by a spring.
    • So the spring force acting upon an object attached to a horizontal spring is given by:
    • The same integration approach can be also applied to the work done by a constant force.
    • In this case, the Pressure (Pressure =Force/Area) is constant and can be taken out of the integral: