Simple harmonic motion and damping

Click For Summary
SUMMARY

The discussion focuses on solving the differential equation representing simple harmonic motion with damping, specifically the equation \(\frac{dr^{2}cos^{2}t}{dt}=rsint\). The key approach involves applying the product rule to differentiate the function \(r=f(t)\) effectively. Participants emphasize the importance of understanding the relationship between the amplitude of oscillation and time in the context of damping effects on harmonic motion.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with simple harmonic motion concepts
  • Knowledge of the product rule in calculus
  • Basic grasp of damping effects in oscillatory systems
NEXT STEPS
  • Study the application of the product rule in solving differential equations
  • Explore the characteristics of simple harmonic motion and its mathematical representation
  • Research damping mechanisms and their impact on oscillatory systems
  • Learn about numerical methods for solving differential equations
USEFUL FOR

Students and professionals in physics and engineering, particularly those studying dynamics, oscillatory systems, and differential equations.

Lamarr
Messages
52
Reaction score
1
I have to solve the following D.E. which describes how the amplitude of oscillation r, changes with time.


[tex]r=f(t)[/tex]



[tex]\frac{dr^{2}cos^{2}t}{dt}=rsint[/tex]



How do I find r?
 
Physics news on Phys.org
Start by applying the product rule.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
Replies
5
Views
2K
  • · Replies 51 ·
2
Replies
51
Views
4K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
Replies
16
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K