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

AI Thread Summary
The discussion revolves around a particle's vibration described by the equation Ut = 8 sin(1/2 pi t/T), indicating an amplitude of 8 cm and a harmonic oscillation. Participants seek to determine the period T, frequency f, and the velocity and acceleration equations by differentiating the original equation. It is clarified that T can be found without differentiation, as it corresponds to the time for the phase to complete one full cycle of 2π. The use of the chain rule is suggested for differentiation to find velocity and acceleration. The conversation emphasizes collaborative problem-solving in physics.
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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