Vibration Question: BoB Released from Rest, Solve for Theta & Vel/Acc at 1.6s

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SUMMARY

The discussion focuses on solving a simple harmonic motion (SHM) problem involving a bob (BoB) released from rest with a length of 102 cm and an initial angle of ±5 degrees under gravitational acceleration of 9.81 m/s². The key equations used include θ = A sin(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase constant. Participants clarify how to determine the period and phase constant, as well as the need to derive θ for velocity and acceleration calculations at 1.6 seconds.

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  • Understanding of simple harmonic motion (SHM)
  • Familiarity with angular frequency (ω) and amplitude (A)
  • Knowledge of basic calculus for deriving functions
  • Ability to apply gravitational equations in physics
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  • Learn how to calculate angular frequency (ω) from the period of SHM
  • Study the derivation of velocity and acceleration in simple harmonic motion
  • Explore the concept of phase constant (φ) in SHM
  • Investigate the effects of varying amplitude (A) on SHM behavior
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Students studying physics, particularly those focusing on mechanics and simple harmonic motion, as well as educators seeking to clarify SHM concepts in classroom settings.

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Homework Statement

:[/B]

BoB released from rest, L = 102 cm, theta = +-5 degrees, g = 9.81 m/s2
assume a SHM
(I) Determine the angle theta after 1.6 s
(II) Determine the magnitudes of velocity & acceleration of the BoB at 1.6 s

Homework Equations



theta = A sin (w t + phai)

The Attempt at a Solution



Does phai represent the period? And how do I get it?
Do I derive theta once & twice? And why?
How do I get w & A?

Thank you!
 
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Hi FChebli! Welcome to PF! :smile:

(have a theta: θ and a phi: φ and an omega: ω :wink:)

θ = A sin(ωt + φ)

A is the maximum value (θ varies between ±A), which you can find from the question

ω is the frequency … to find the period, you need the value of t which makes (ωt + φ) increase by 2π

φ is the phase … it's often zero, but not always … you find it by putting t = 0, and seeing what θ is (or dθ/dt, if that's given instead) :wink:
 
Thank you so much! :)
 

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