Mass attached to a horizontal spring

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SUMMARY

The discussion centers on the motion of a particle with a mass of 0.210 kg attached to a horizontal spring with a force constant of 0.84 N/m. The particle reaches a maximum speed of 5 m/s at time t=0, moving to the left. The correct equation of motion for the particle is determined to be x(t) = (5/2)Sin(2t + π), indicating simple harmonic motion. The user successfully isolates the position function after initial confusion regarding the application of Newton's second law and Hooke's law.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Familiarity with Hooke's law (F = -kx)
  • Knowledge of Newton's second law (F = ma)
  • Basic trigonometric functions and their applications in physics
NEXT STEPS
  • Study the derivation of the equation of motion for simple harmonic oscillators
  • Learn about energy conservation in harmonic motion
  • Explore the effects of varying mass and spring constants on oscillation frequency
  • Investigate the damping effects on harmonic motion
USEFUL FOR

Students of physics, mechanical engineers, and anyone interested in understanding the dynamics of oscillatory systems and simple harmonic motion.

pvpkillerx
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A particle with a mass of 0.210kg is attached to a horizontal spring with a force constant of 0.84 N/m. At the moment t=0, the particle has its maximum speed of 5m/s and is moving to the left. (Assume that the positive direction is to the right.)

Determine the particle's equation of motion, specifying its position as a function of time (use the following as necessary: t)

F = -kx
F = ma




What I did was:
-0.84x = 0.210a
-0.84x = 0.210[(v - 5)/t)]
-0.84x = 0.210[(x/t - 5)/t]


I still can't isolate for x, and i don't know if what i am doing is right. Please help.
 
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nvm, i figured it out, its 5/2Sin(2t+pi)
 

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