Finding Force and Distance in Simple Harmonic Motion Problem

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SUMMARY

The discussion focuses on calculating the force between a block and the bottom of a box in a simple harmonic motion scenario involving a spring. The system consists of a box with mass M and a block with mass m, suspended by a spring with stiffness k. The key equations used include F(m+M)=mg+ma and x(t)=dcos(ωt), where ω=√(k/(m+M)). The challenge lies in determining the reaction force as a function of time and identifying the critical distance d at which the block begins to leave the bottom of the box during vertical oscillations.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with Newton's second law of motion
  • Knowledge of spring mechanics and Hooke's law
  • Ability to solve differential equations related to oscillatory motion
NEXT STEPS
  • Study the derivation of the force function in oscillatory systems
  • Explore the concept of critical damping in spring-mass systems
  • Learn about energy conservation in simple harmonic motion
  • Investigate the effects of varying mass and spring stiffness on oscillation frequency
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to enhance their understanding of simple harmonic systems.

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Homework Statement


A box of mass M is suspended by a spring of stiffness k. A small block of mass m is placed inside the box. If the system is pulled downward by a distance d and then released from rest:

a.) find the force between the bottom of the box and the block as a function of time;
b.) for what value of d does the block just begin to leave the bottom of the box at the top of the vertical osscilations?


Homework Equations


F(m+M)=mg+ma
x(t)=dcos(ωt)
ω=√(k/(m+M)).


The Attempt at a Solution


I'm unsure of how to proceed to determine the force of reaction from the equations above that I've worked out.
 
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