Solving SHM: Find Amplitude, Velocity & Time

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SUMMARY

The discussion focuses on solving a simple harmonic motion (SHM) problem involving a body with specific velocities at given distances from the mean position. The key equations mentioned include the position function x = A sin(ωt) and the need to derive the velocity function. The amplitude of the motion, velocity at the mid-position, and the time elapsed between two specific velocities are the primary objectives of the problem. Participants emphasize the importance of using consistent formulas and suggest that graphical representation may aid in understanding the motion.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Familiarity with trigonometric functions and their applications in physics
  • Knowledge of the relationship between position, velocity, and time in SHM
  • Ability to manipulate and solve equations involving sine functions
NEXT STEPS
  • Study the derivation of velocity as a function of time in SHM
  • Learn how to calculate amplitude from velocity and position data
  • Explore the concept of angular frequency (ω) in SHM
  • Investigate graphical methods for visualizing SHM and its parameters
USEFUL FOR

Students and educators in physics, particularly those focusing on mechanics and oscillatory motion, as well as anyone seeking to deepen their understanding of simple harmonic motion principles.

ZackGardner
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A body with SHM has a velocity of 1.3 m/s at a distance of 1.0m from the mean position, and a velocity of 1.0 m/s at a distance of 1.3m from the mean position. Find:

a) The amplitude of the motion.
b) The velocity of the mid-position.
c) The time elapsed between the instants when the body is moving at 1.0 m/s and when it is moving at 1.3 m/s.

Can anyone help me, I have been looking on the internet for formulas but I keep getting websites with different ones & don't know which ones to use. Do I need to draw a graph to answer any part of the question too cheers :)
 
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Hints: Start with the equation for position as a function of time:
x = A sin(ωt)

How would you write the speed as a function of time?
 
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