Simple Harmonic Motion: Calculate Max Velocity

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SUMMARY

The discussion focuses on calculating the maximum velocity of a mass in simple harmonic motion (SHM) using energy conservation principles. A mass of 0.4 kg attached to a spring with a spring constant of 80 N/m and a starting displacement of 0.10 m is analyzed. The correct maximum velocity at the equilibrium point is determined to be 1.4 m/s, contrasting with an incorrect calculation of 2 m/s. The key takeaway is the importance of using energy conservation rather than uniform acceleration equations in SHM problems.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Familiarity with Hooke's Law and spring constants
  • Knowledge of energy conservation principles in physics
  • Basic skills in solving quadratic equations
NEXT STEPS
  • Study the principles of energy conservation in mechanical systems
  • Learn how to derive maximum velocity in SHM using potential and kinetic energy equations
  • Explore the relationship between spring constant and mass in SHM
  • Investigate the effects of varying amplitude on maximum velocity in SHM
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and simple harmonic motion, as well as educators looking for practical examples of SHM calculations.

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Homework Statement


A mass of 0.4 kg, hanging from a spring (k= 80N/m) is set into an up-and-down SHM. What is the speed of the mass when moving through the equilibrium point? The starting displacement, A, is 0.10 m.

Homework Equations


a = -kx/m
ω = 2pi/T

The Attempt at a Solution


I tried to apply one of the equations of motion: 2ax = vf^2 - vi^2: but I got an answer of 2 m/s, which is incorrect as the correct answer is 1.4 m/s. Now, I realize that acceleration is not uniform which means that I can't use that equation.
However, I'm not sure what else to do. Using a = -kx/m I managed to calculate the acceleration at the equilibrium point, but without any sort of time or time period or frequency, I haven't a clue how to solve this question.
 
Last edited:
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Use energy conservation.
 

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