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

In summary, the equation given has an amplitude of 8 cm and is a sine function, indicating harmonic oscillation. The individual is seeking to find the time for one oscillation (T) and the frequency (f), which is 1/T. They also need help differentiating the given equation to find the equations for velocity (Vt) and acceleration (At), as well as the velocity and acceleration at t = 1s. They also want to find the maximum velocity (Vmax) and acceleration (Amax).
  • #1
sam2711
2
0
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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  • #2
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:​
 
  • #3
thanks for the help tiny-tim, will post my work as soon as I'm done
 

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

1. What does the equation "Ut = 8 sin (1/2 pi t/T)" represent?

The equation represents the position of a particle that is vibrating with a frequency of 1/2 pi t/T, where t is time and T is the period of the vibration. The amplitude of the vibration is 8 units.

2. How does the frequency of the vibration affect the particle's motion?

The frequency of the vibration determines how quickly the particle moves back and forth. A higher frequency results in a faster motion, while a lower frequency results in a slower motion.

3. Can you explain what "1/2 pi t/T" means in the equation?

The value of 1/2 pi t/T represents the angular frequency of the particle's vibration. It is calculated by dividing the actual frequency by the period of the vibration.

4. How is the position of the particle calculated at a specific time using this equation?

To calculate the position of the particle at a specific time, plug in the value of t into the equation and solve for Ut. This will give you the position of the particle at that time.

5. What are the units of measurement for the variables in this equation?

The unit for time (t) is usually seconds, while the unit for frequency (f) is hertz (Hz). The period (T) can also be measured in seconds. The position (Ut) is measured in units of distance, such as meters or centimeters.

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