The equation for Hooke's Law is F = -kx, where F is the force applied, k is the spring constant, and x is the displacement of the spring. How does the spring constant affect the force applied? The spring constant, k, represents the stiffness of the spring. A higher spri...
For Hooke’s Law to work properly, the parts of the equation have to be in the correct units. Without consistent units, the equation is meaningless. You can set the gravitational force exerted by the mass on the spring equal to the force exerted by the spring due to Newton’s Third Law...
The equation describing this relationship describes the restoring force F that the spring exerts against the external force causing deformation. The restoring force is customarily negative to indicate it is the opposite direction of the force acting on the object, as it resists the deformatio...
ξ=X−X0;withX0=MΩ2LK−Ω2M X0 is the spring elongation which allows one to balance the permanent centrifugal force. Accordingly, the force equation is re-written as: Mξ¨+(K−Ω2M)ξ=0 As written in terms of X, the equation describes the axial motion of the mass reference...
A simple spring-mass model is used to calculate the contact force-time relationship during hard impact. The non-linear spring stiffness in the contact zone is estimated from static penetration resistance tests, and the differential equation of equilibrium is solved numerically for an initial impact ...
Problem Statement: A known mass at a know velocity collides on a spring of known stiffness. What is the equation that governs the deceleration of the mass, so that the force on the spring could be found? Relevant Equations: 1/2 m*V^2 = 1/2*k*x^2 + 1/2*m*(Vo)^2 Kinetic energ...
As expected, this implies that the mass and spring oscillations occur more slowly with respect to the relatively-moving primed coordinates. On the other hand, the equation of motion (in the y′ direction) with respect to these coordinates has the same form as it does with respect to the ...
As the deformation of the torsion spring increases, the driving force decreases until the sliding ceases. This process repeats cyclically. The vibration phenomenon induced by this stick–slip process is referred to as self-excited friction vibration. According to Equation (29), when the system’s ...
Hooke's Law Equation Hooke's law states that the restoring force is directly proportional to the spring's displacement. It was formulated by the English scientist Robert Hooke in 1660 while working on the designs for the balance springs of clocks. It is expressed as: {eq}F=-kx {/eq} ...
Equation Generation: Mass-Spring-Damper. This is a mass-spring-damper system modeled using multibody components. The simulation results window shows the x position of the mass versus time as well as the 3-D playback of the oscillating mass. The equati