A spring of stiffness k supports a box of mass M in which is placed a block of mass m the system is pulled downward a distance d from the equilibrium position and ti released, find the force of reaction between the block and the bottom of the box as a fu

A spring of stiffness k supports a box of mass M in which is placed a block of mass m the system is pulled downward a distance d from the equilibrium position and ti released, find the force of reaction between the block and the bottom of the box as a fu

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter3: Oscillations

Section: Chapter Questions

Problem 3.31P

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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

Analytical Mechanics

A spring of stiffness k supports a box of mass M in which is placed a block of mass m. If
the system is pulled downward a distance d from the equilibrium position and then
released, find the force of reaction between the block and the bottom of the box as a func-
tion of time. For what value of d does the block just begin to leave the bottom of the box
at the top of the vertical oscillations? Neglect any air resistance.
3.8

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