About the formula of pendulum -- What if there is damping?

Click For Summary
SUMMARY

The discussion focuses on correcting the formula for a damped pendulum, specifically addressing the equation a(t) = a0 * sin(sqrt(g/l) * t * Pi/2) - [k/(m*l*l) * cos(sqrt(g/l) * t * Pi/2) * t]. The user identifies that the current formula does not account for damping, resulting in a constant curve. The proposed solution involves modifying the second part of the equation to ensure the curve decreases over time, ultimately leading to a more accurate representation of a damped pendulum's motion. The suggestion to explore the damped harmonic oscillator is also highlighted as a potential avenue for correction.

PREREQUISITES
  • Understanding of basic pendulum mechanics
  • Familiarity with differential equations
  • Knowledge of damping in oscillatory systems
  • Experience with mathematical modeling in physics
NEXT STEPS
  • Research the equations governing damped harmonic oscillators
  • Study the effects of friction on pendulum motion
  • Explore numerical methods for solving differential equations
  • Investigate the impact of varying parameters (k, m, l) on pendulum behavior
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of oscillatory systems, particularly those studying the effects of damping on pendulum motion.

karimce
Messages
1
Reaction score
0
http://physics.stackexchange.com/questions/243457/about-the-formula-of-pendulum-simple

a(t) = a0 * sin ( sqrt(g/l) * t * Pi/2 ) - [ k/(mll) * cos ( sqrt(g/l) * t * Pi/2 ) * t ) ]

a(t) : the angle in instant t .
t : time
g : gravity .
Pi = 3.14
k = Fixed (Friction )
l : longer of pendulum

but this formula is wrong , because the curve of this formula Remains constant , like this :
K9i9f.png


I want to correct this equation to become true Means keeps decreasing curve, even non-existent ( = 0 ) .
lwTAG.png

Specifically I want to change in the second part , in [ k/(m*l*l) * cos ( sqrt(g/l) * t * Pi/2 ) * t ) ]

can you help me ? Are there any other equation?
 

Attachments

  • K9i9f.png
    K9i9f.png
    8.8 KB · Views: 461
Last edited by a moderator:
Physics news on Phys.org

Similar threads

  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K