Differential equation of motion

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SUMMARY

The discussion focuses on determining the maximal ground reaction force in the context of a differential equation of motion, specifically when the initial speed (Vo) is zero. The equation of motion is represented as Y1(t) = A sin(ωt) + B cos(ωt) + g/ω², where ω is defined as √(k/m). The challenge lies in identifying the appropriate initial conditions to solve for constants A and B, given that y=0 and Vo=0, with no x component present.

PREREQUISITES
  • Understanding of differential equations, particularly in motion dynamics.
  • Familiarity with harmonic motion and its mathematical representation.
  • Knowledge of initial conditions and their role in solving differential equations.
  • Basic grasp of physical concepts such as ground reaction forces and body weight (mg).
NEXT STEPS
  • Study the derivation and application of the harmonic oscillator equation in physics.
  • Learn about initial condition problems in differential equations.
  • Explore the concept of ground reaction forces in biomechanics.
  • Investigate the relationship between mass, spring constant, and angular frequency in oscillatory motion.
USEFUL FOR

This discussion is beneficial for physics students, mechanical engineers, and anyone studying dynamics and motion analysis, particularly in the context of biomechanics and differential equations.

Lozzakw
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Homework Statement



Find the maximal ground reaction force for the limiting case where the speed at initial contact is equal 0 (Vo=0) expressing it as a mulitple of the body weight (mg)
ω = √k/m

Homework Equations



Y1(t) = A sinωt + B cos ωt + g/ω^2

The Attempt at a Solution



I know A and B are constants based on the initial conditions but as y=0 and Vo= 0 and there is no x componant - what other initial conditions can I use?
 
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