Finding the angle of a pendulum in SHM

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SUMMARY

The discussion focuses on calculating the angle of a pendulum undergoing simple harmonic motion (SHM) with a frequency of 1.5 Hz and an initial angle of 20° from the vertical. The period (T) is determined to be approximately 0.67 seconds. Using the equation θ = 20*cos(2πt/T), the angle at t = 0.25 seconds is derived, emphasizing the importance of distinguishing between the angle of swing and the cosine argument.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Knowledge of trigonometric functions, particularly cosine
  • Familiarity with frequency and period calculations
  • Ability to manipulate equations of motion in physics
NEXT STEPS
  • Study the derivation of the equations of motion for simple harmonic oscillators
  • Learn about the effects of damping on pendulum motion
  • Explore the relationship between frequency and period in oscillatory systems
  • Investigate the application of SHM in real-world scenarios, such as clocks and pendulums
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for examples of simple harmonic motion applications.

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Homework Statement


A clock pendulum oscillates at a frequency of 1.5 Hz. At t = 0, it is released from rest starting at an angle of 20° to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at the following times? (Hint: Do not confuse the angle of swing θ of the pendulum with the angle that appears as the argument of the cosine.)
Find the angle at t = 0.25 s



Homework Equations



T=1/f x=Acos(2pit/T) feta=2pi(t/T)

The Attempt at a Solution


T=1/1.5 T=.67sec feta=2pi(.25sec/.67)
 
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Pay attention to that hint! In this question, the amplitude is 20 degrees and equation of motion gives the angle at other times:
θ = 20*cos(2πt/T)
 

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