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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.
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
Suppose a mass m is attached to the end of a spring of force constant k (whose other end is fixed) and slides on a frictionless surface. This system is illustrated in Fig. 4.2.
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.
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)
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
In these notes, we introduce simple harmonic oscillator motions, its defining equation of motion, and the corresponding general solutions. We discuss how the equation of motion of the pendulum approximates the simple harmonic oscillator equation of motion in the small angle approximation.
