What Are the Amplitude and Period of the Mass-Spring System?

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SUMMARY

The discussion focuses on calculating the amplitude and period of a mass-spring system with a spring constant of k=74 N/m and a mass of 490g. The user employs the formula F = -kx and attempts to express displacement as x = A cos(ωt), where ω is the angular frequency. To find the amplitude A, the user is advised to determine ω using the formula ω = √(k/m) and to recognize that at maximum displacement, the velocity is zero, which simplifies the calculations.

PREREQUISITES

  • Understanding of Hooke's Law and spring constant (k)
  • Knowledge of angular frequency (ω) in oscillatory motion
  • Familiarity with the concepts of amplitude and period in harmonic motion
  • Basic algebra for manipulating equations involving trigonometric functions

NEXT STEPS

  • Calculate the angular frequency ω using the formula ω = √(k/m)
  • Determine the period T of the mass-spring system using T = 2π/ω
  • Explore the relationship between maximum displacement and velocity in harmonic motion
  • Investigate the effects of varying the mass and spring constant on the system's behavior

USEFUL FOR

Students and educators in physics, mechanical engineers, and anyone studying oscillatory systems and harmonic motion.

teenholiday
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A massless sping of spring constant k=74 N/m is hanging from the ceiling. A 490g mass is hooked onto the unstretched spring and allowed to drop. Find the amplitude and the period of the resulting motion.

Attempt:
F= -kx

x= A cos (wt)
w = sqrt(k/m) t

I'm trying to solve for A, but how do I get rid of the t variable?


Thanks
 
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Find [itex]\omega[/itex] and you could use the fact that at max displacement from the equilibrium posistion, velocty=0.
 

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