How Do You Solve Periodic Motion Problems in Physics?

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SUMMARY

This discussion focuses on solving periodic motion problems in physics, specifically addressing frequency and angular frequency units, pendulum design for a 1-second period, and the effects of amplitude on oscillation periods. The correct unit for frequency is hertz (Hz), equivalent to cycles per second, while angular frequency is measured in radians per second. For a pendulum to achieve a period of 1 second, its length should be approximately 0.25 meters. The period of a mass oscillating on a spring remains 2 seconds regardless of amplitude changes, as the period is independent of amplitude.

PREREQUISITES
  • Understanding of basic physics concepts, particularly periodic motion
  • Familiarity with the formula T=(2π) * √(mass/k) for oscillation periods
  • Knowledge of the relationship between frequency and angular frequency
  • Ability to perform unit conversions and calculations involving square roots
NEXT STEPS
  • Study the derivation of the formula for the period of a pendulum
  • Learn about the relationship between frequency, period, and angular frequency
  • Explore the effects of damping on oscillatory motion
  • Investigate different types of oscillators, such as simple harmonic motion and damped oscillations
USEFUL FOR

Students studying physics, educators teaching periodic motion, and anyone interested in understanding the principles of oscillation and wave mechanics.

SoulInNeed
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Please help with periodic motion problems!

1. What are the correct units for frequency? What are the correct units for angular frequency?

2. A grandfather clock keeps time by using a pendulum. If you want to design a pendulum to have a period of 1 s, estimate how long you should make the pendulum.

3.A mass oscillating on a given spring has a period of 2s. The spring is now stretched to have an oscillation amplitude that is twice its original amplitude. Which of the following is true?

The period is 0.5 s.
The period is 1 s.
The period is 2 s.
The period is 2.8s
The period is 4s.

4. Explain your answer to the multiple choice question above.



Homework Equations

T=(2*pi) * The square root of mass/constant force k
T=(2*pi) * Square root of Length/gravity



3. 1. The correct unit for frequency is the hertz, and 1 hertz is equal to 1 cycle per second. The angular frequency is the rate of change of angular quantity that is always measured in radians, and its units are radians/seconds.

2. 1=(2*pi) * The square root of Length divided by gravity
.159=The square root of length divided by gravity
.025=L/g
.25 m=Length

3. The period is 2 s

4. The period does not depend on amplitude.

Thanks!
 
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It is correct.

ehild
 

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