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The k in the Hooke’s law equation is known as the spring constant. This is a measure of the stiffness of the spring. Say you have two different springs and you stretch them the same amount from equilibrium. The one that requires more force to maintain that stretch has the larger spring constant.
6 Νοε 2014 · Hooke’s Law states that: FS = k x (9.1) Here k is the spring constant, which is a quality particular to each spring, and x is the distance the spring is stretched or compressed. The force FS is a restorative force and its direction is opposite (hence the minus sign) to the direction of the spring’s displacement x.
13 Ιαν 2017 · Today you will measure the spring constant (k) of a given spring in two ways. First, you will gradually add mass (m) to the spring and measure its displacement ( x) when in equilibrium; then using Hooke’s law and Eq. 10.2 you will plot FS vs. xto nd the spring constant. Second, you
= spring constant [kg· m2/s2] N = Friction coefficient [kg· m2/s] The solution to equation (1) is standard. It can be found in any general mechanics or calculus lecture. Here, we will give the main results that satisfy the equation, as well as the corresponding physical interpretations of our rotating pendulum. If we define: l = N
This equation of motion, Eq. (23.2.1), is called the . simple harmonic oscillator equation (SHO). Because the spring force depends on the distance . x, the acceleration is not constant. Eq. (23.2.1) is a second order linear differential equation, in which the second
springs (or, in practice, for small displacements) the relationship is linear: =−𝑘𝑥 (1) 𝑘 –is called the stiffness or spring constant. It is measured in newtons per metre (N m 1). The equation of motion is then 𝑚 d2𝑥 d 2 =−𝑘𝑥 (2) To solve (2) note that d 2𝑥/d =−(𝑘/𝑚)𝑥 and that 𝑘/𝑚 is a positive ...
Figure 4.1: Harmonic Oscillation of a mass at a spring. At the maximum elongation the spring is pulling on the mass. The mass gets accelerated towards the equilibrium position. At the equilibrium position the acceleration is zero and the velocity of the mass reaches its maximum.
