What is the maximum kinetic energy for harmonic motion with a reduced amplitude?

Click For Summary
SUMMARY

The maximum kinetic energy (KE) for harmonic motion with a reduced amplitude is determined by the formula KE = 1/2 k A², where A represents the amplitude. In the discussion, a miscalculation was noted regarding the maximum KE when the amplitude is reduced to one third of its original value. The correct approach requires clear visibility of the working steps for accurate assessment. Participants are encouraged to present their calculations in a structured manner for clarity.

PREREQUISITES
  • Understanding of harmonic motion principles
  • Familiarity with kinetic energy formulas
  • Basic algebra skills for manipulating equations
  • Ability to interpret and present mathematical solutions clearly
NEXT STEPS
  • Review the derivation of kinetic energy in harmonic motion
  • Study the effects of amplitude changes on kinetic energy
  • Learn about the conservation of energy in oscillatory systems
  • Explore examples of harmonic motion problems with varying amplitudes
USEFUL FOR

Students studying physics, educators teaching harmonic motion concepts, and anyone interested in the mathematical foundations of kinetic energy in oscillatory systems.

Frouel
Messages
8
Reaction score
0
Homework Statement
Before the rocket launch, the pendulum suspended in the cockpit made vibrations with the oscillation period of 2 s. During the vertical launch of the rocket, it was noticed that the pendulum made 5 oscillations in 6 s. Calculate the acceleration of the rocket. g = 10m / s2

The maximum kinetic energy of a harmonically vibrating body is 10mJ. Calculate its kinetic energy when the pendulum deflection is A / 3, where A - vibration amplitude

A stone was released into the shaft, which hit the bottom with a velocity of v = 40 m / s2. Assuming that the stone falls with the acceleration due to gravity g = 10 m / s2 and the voice velocity in the air is 340 m / s, calculate the time after which we will hear the stone knock against the bottom of the shaft.
Relevant Equations
Associate with simple harmonic motion and waves.
Solutions in a file.
 

Attachments

  • F747DC49-BC46-4130-A71E-AFDC89F77A43.jpeg
    F747DC49-BC46-4130-A71E-AFDC89F77A43.jpeg
    69.2 KB · Views: 159
  • 534945D1-19BF-4F49-A1CF-280C211FA0E3.jpeg
    534945D1-19BF-4F49-A1CF-280C211FA0E3.jpeg
    69.9 KB · Views: 158
  • FDFF44B2-9EAA-4875-8514-EDF97783B250.jpeg
    FDFF44B2-9EAA-4875-8514-EDF97783B250.jpeg
    64.9 KB · Views: 160
Physics news on Phys.org
You haven't answered question 1. I'm not sure what you've done for question 2, but the answer seems wrong. Your working for question 3 is not visible.
Make some effort and type out your working.
 
Further to the response above, please use a separate thread for each unrelated problem.
In question 2, you have calculated what the maximum KE would be if the amplitude were only one third. That is not what you are asked.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 13 ·
Replies
13
Views
1K
Replies
5
Views
1K
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
3
Views
861
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
16
Views
2K