Why does the period increase when the string length is increased?

Click For Summary
SUMMARY

The discussion centers on the relationship between the length of a spring and its period, establishing that the period is proportional to the square root of the string length. As the length increases, the distance the mass must travel also increases, resulting in a longer period for each cycle. The mathematical derivation confirms that T = 2π√(r/a), where T is the period, r is the length, and a is the acceleration. This relationship is crucial for understanding oscillatory motion in systems resembling pendulums.

PREREQUISITES
  • Understanding of basic physics concepts such as oscillatory motion and pendulum dynamics.
  • Familiarity with mathematical equations involving acceleration and period.
  • Knowledge of the relationship between force, mass, and acceleration.
  • Basic algebra skills for manipulating equations.
NEXT STEPS
  • Study the principles of harmonic motion in more detail.
  • Learn about the effects of mass and amplitude on the period of oscillation.
  • Explore the mathematical derivation of pendulum motion using calculus.
  • Investigate real-world applications of spring dynamics in engineering.
USEFUL FOR

Students of physics, educators teaching mechanics, and engineers involved in designing oscillatory systems will benefit from this discussion.

dumb
Messages
6
Reaction score
0
hey,

i have to do an experiment about length of spring and its period, found the relationship, the period is proportional to the square root of the string length. (looks like a pendelum) but i don't understant why when u increase the length, the period increases! tell me y please! urgent :confused:
 
Physics news on Phys.org
By increasing the length of the string, you increase the distance the needed to travel. So even though you have not changed the amplitude or the mass at the end of the string it will still take longer to travel that distance. Simply, it takes longer to complete one cycle if it has further to travel if the speed is not changed.
 
You have to know if the speed stays the same, the force stays same or neither in order to see the relation. But since you say mention squareroot, i'll presume the force is the same.

acceleration 1= acceleration 2
acceleration=v^2/r
v=2*PI*r/T

So
acceleration=(2*PI*r/T)^2/r
=4*PI^2*r^2/T^2r
=4*Pi^2*r/T^2

So

T^2=4*Pi^2*r/a
T=2*PI*r^0.5/a^0.5

So this is the relation with the square root of the radius.
 
Nice mathematical explanation! :smile: Dumb, does that help you?
 
Dumb, if you do it on paper you'll understand better.
 
THANK U SOO MUCH EVERYONE :biggrin: :biggrin: , i did understand!
 

Similar threads

Undergrad Stable solutions to simplified 2- and 3-body problems?
  • · Replies 6 ·
Replies
6
Views
3K
Waves -- How does increasing tension affect frequency and period?
  • · Replies 2 ·
Replies
2
Views
4K
Guitar string tension: effect of total length - continued
  • · Replies 5 ·
Replies
5
Views
2K
High School Why Does a Spring Return to Its Original Position After Being Stretched?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Mechanism of Energy Conservation in Zero-Amplitude Sum of EM Waveforms
  • · Replies 21 ·
Replies
21
Views
2K
Conical Pendulum with varying string length
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Why does a guitar string "beat" as if it is out of phase?
  • · Replies 11 ·
Replies
11
Views
3K
How Is the Period of a Pendulum Affected by Its Length?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Is "nondimensionalization" a misnomer?
  • · Replies 19 ·
Replies
19
Views
2K
Measurement and Graphing. Dependence of a Pendulum on length
  • · Replies 1 ·
Replies
1
Views
1K