Object Oscillation: Vmax & Amax Known

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SUMMARY

The discussion centers on the oscillation of an object attached to a horizontal spring, specifically analyzing the relationship between maximum speed (Vmax) and maximum acceleration (Amax). The maximum speed is given as 1.11 m/s, while the maximum acceleration is 6.65 m/s². It is established that Vmax occurs at the equilibrium position (x=0), and Amax occurs at the maximum displacement (xmax). The participants emphasize the need to differentiate the equations of simple harmonic motion to determine the time interval between these two maximums.

PREREQUISITES
  • Understanding of simple harmonic motion equations
  • Familiarity with differentiation in calculus
  • Knowledge of energy conservation principles in oscillatory systems
  • Ability to identify maximum speed and acceleration in oscillatory motion
NEXT STEPS
  • Study the equations of motion for simple harmonic oscillators
  • Learn how to differentiate trigonometric functions to find maxima and minima
  • Explore energy conservation in oscillatory systems
  • Investigate the relationship between displacement, velocity, and acceleration in harmonic motion
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts of simple harmonic motion.

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Homework Statement



An object attached to a horizontal spring is oscillating back and forth along a frictionless surface. The maximum speed of the object is 1.11 m/s, and its maximum acceleration is 6.65 m/s2. How much time elapses between an instant when the object's speed is at a maximum and the next instant when its acceleration is at a maximum

Homework Equations





The Attempt at a Solution



Not sure where to start
 
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You can use equation for a simple harmonic motion (distance as a cosine or sine function), and keep differentiating it to find the time of maximum speed and acceleration.
 
or use energy conservation

at which position do you think speed and acc. be max
 
Still not getting it..
 
cupid.callin said:
or use energy conservation

at which position do you think speed and acc. be max

Vmax will occur when x=0

Amax will occur when V=0
 
Student3.41 said:
Vmax will occur when x=0

Amax will occur when V=0

V is not a position.
 
gneill said:
V is not a position.

well Amax will occur at xmax
 
Jow can you write the energies of body at x=0 and x=max?
 
Student3.41 said:
well Amax will occur at xmax

Yes, and what position is that, where position means angle(s).
 
  • #10
Still not understanding can you lay it out a bit
 
  • #11
In simple harmonic motion the displacement follows a sine (or cosine, your choice) function. You should have seen this in class or in your text.
 

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