Understanding Oscillatory Motion: Relationship Between Length and Time

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SUMMARY

The discussion focuses on the fundamentals of oscillatory motion, specifically the relationship between the length of a string (L) and the period of oscillation (t). Participants confirm that the relationship is expressed as t ∝ √L, indicating that the period increases with the square root of the length. A force diagram is recommended to derive the equation governing simple harmonic motion (SHM) for a ruler suspended and oscillating at an angle. This foundational understanding is crucial for analyzing oscillatory systems.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Familiarity with force diagrams and their applications
  • Basic knowledge of oscillatory systems and pendulum mechanics
  • Ability to manipulate mathematical relationships involving square roots
NEXT STEPS
  • Study the derivation of the SHM equation for oscillating systems
  • Explore the effects of varying string lengths on oscillation periods
  • Learn about the principles of pendulum motion and its applications
  • Investigate the impact of angle on the period of oscillation in SHM
USEFUL FOR

Students and educators in physics, engineers working with oscillatory systems, and anyone interested in the principles of motion and dynamics.

Black-Enigma
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Hi everyone,

Could someone please help me with the fundamentals of oscillatory motion.

A 1 metre ruler is suspended on both ends by two strings attatched to retort stands. The length of the string is increased to observe the increase in period of oscillation.

I need to know the relationship between L (length of string) and t (time)

I am guessing the relationship is t : √L

Thanks

p.s I need the answer ergently
 
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Welcome to PF!

Black-Enigma said:
I am guessing the relationship is t : √L

Hi Black-Enigma ! Welcome to PF! :smile:

Guessing is no good! :rolleyes:

(is the rule moving parallel to its length, or sideways? :confused:)

Hint: do a force diagram to work out the force at a typical angle.

That will give you an SHM equation, and the coefficient will tell you the relationship between L and t. :smile:
 
Hi tinytim, the ruler is being rotated about 45 degrees and then released. It oscillates back and forth.

thanks
 

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