What Values of C Cause Resonance in a Linear System with Given Solutions?

Click For Summary
SUMMARY

The discussion centers on determining the values of the constant C that cause resonance in a linear system defined by the complementary solution A(coswt, coswt-wsinwt) + B(sinwt, wcoswt+sinwt) and the forcing term (coswt, coswt-Csinwt). It is established that resonance occurs for any value of C, emphasizing that the frequency variable "w" is the critical factor influencing resonance, rather than the value of C itself.

PREREQUISITES
  • Understanding of linear systems and their solutions
  • Familiarity with resonance phenomena in differential equations
  • Knowledge of trigonometric functions and their applications in physics
  • Basic concepts of forcing terms in linear systems
NEXT STEPS
  • Study the role of frequency "w" in resonance within linear systems
  • Explore the mathematical derivation of complementary solutions in differential equations
  • Investigate the impact of different forcing terms on system behavior
  • Learn about the conditions for resonance in various physical systems
USEFUL FOR

Students and professionals in physics, engineers working with dynamic systems, and mathematicians focusing on differential equations will benefit from this discussion.

lukepeterpaul
Messages
14
Reaction score
0
Hi,
Say if the complementary solution to a linear system is
A(coswt, coswt-wsinwt)+B(sinwt, wcoswt+sinwt)
and the forcing term is (coswt, coswt-Csinwt), where C is constant
How do I tell whether for what values of C is resonance going to occur?
Thanks!
 
Physics news on Phys.org


Resonance will occur for any value of C. It is the "w" that is important, not C.
 


Thanks, HallsofIvy. :)
 

Similar threads

Undergrad Find Practical Resonance Frequencies in Linear Differential Equations
  • · Replies 1 ·
Replies
1
Views
3K
Difference between resonance in undamped vs damped mass-spring-dashpot
  • · Replies 17 ·
Replies
17
Views
3K
Graduate Pair of interacting systems, driven coupled harmonic oscillators
  • · Replies 7 ·
Replies
7
Views
2K
Rolling without slipping problem
  • · Replies 42 ·
2
Replies
42
Views
4K
Resonance Frequency Homework: Find Frequency w/Given Spring & Mass
  • · Replies 17 ·
Replies
17
Views
4K
Graduate Resonant frequencies of liquid in a cylinder
  • · Replies 14 ·
Replies
14
Views
3K
Damped Harmonic Oscillator and Resonance
  • · Replies 9 ·
Replies
9
Views
7K
At what angular frequencies is the amplitude half of its resonant value?
  • · Replies 1 ·
Replies
1
Views
2K
2nd order resonance filter amplitude response(z-parameters)
  • · Replies 14 ·
Replies
14
Views
2K
Admissions Could I please get critique on my SOP? (Experimental Biophysics)
  • · Replies 9 ·
Replies
9
Views
2K