A particle is vibrating with f : Ut = 8 sin (1/2 pi t/T)

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SUMMARY

The discussion centers on the analysis of the harmonic oscillation described by the equation Ut = 8 sin(1/2 π t/T). The amplitude is confirmed to be 8 cm, and participants seek to determine the period T, frequency f, and the equations for velocity (Vt) and acceleration (At). Key insights include that the period T corresponds to the time for one complete oscillation, which occurs when the phase reaches 2π. Additionally, the chain rule is recommended for differentiating the equation to find velocity and acceleration.

PREREQUISITES
  • Understanding of harmonic oscillation principles
  • Knowledge of sine functions and their properties
  • Familiarity with differentiation techniques, specifically the chain rule
  • Basic concepts of velocity and acceleration in physics
NEXT STEPS
  • Calculate the period T from the given equation Ut = 8 sin(1/2 π t/T)
  • Determine the frequency f using the relationship f = 1/T
  • Differentiate the equation Ut to find the velocity Vt and acceleration At
  • Explore maximum velocity (Vmax) and maximum acceleration (Amax) for harmonic oscillators
USEFUL FOR

Students and enthusiasts of physics, particularly those studying harmonic motion, as well as educators seeking to clarify concepts related to oscillations and differentiation in physical equations.

sam2711
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from this equation i get the amplitude is 8 cm, it's a sine function so i guess it has to be a harmonic oscillation

i haven't had physics in a while so not really getting anywhere

-i need to know T (time for one oscillation)
-the frequency f which is 1/T
-Vt and At equations, i know i have to differentiate the given equation but i can't figure out how exactly
-the velocity (speed) and acceleration on t = 1s
-and the Vmax and Amax
 
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hi sam2711! welcome to pf! :smile:
sam2711 said:
i need to know T (time for one oscillation)

you don't need to differentiate for that …

the period T is the the value of t for which the angle (the phase) is 2π (= 360°) :wink:

… i know i have to differentiate the given equation but i can't figure out how exactly

use the chain rule …

show us what you get :smile:​
 
thanks for the help tiny-tim, will post my work as soon as I'm done
 

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