Converting periodic function from radians to time?

In summary, the homework exercise involves converting a periodic function in radians into a periodic function in time. After substitution and some logical reasoning, the function was simplified to (160t)/(∏ * T) for -T/4 ≤ t ≤ T/4 and (80T -160)/(∏ * T) t for T/4 ≤ t ≤ 3T/4. However, this function is not periodic and the range needs to be modified to reflect the periodicity.
  • #1
jean28
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Homework Statement


Hey guys. So I have this homework exercise where I have to convert the following periodic function in radians into a periodic function in time.

f(θ) = (80/∏2) θ, -∏/2 ≤ θ ≤ ∏/2
(80/∏) - (80/∏2) θ, ∏/2 ≤ θ ≤ 3∏/2

Homework Equations



θ = ω0 t
ω0 = 2∏/T

The Attempt at a Solution



After substituting the relevant equations into the original equation and using a bit of logic regarding the periods and time intervals, I got the following function:

(160t)/(∏ * T) , -T/4 ≤ t ≤ T/4
(80T -160)/(∏ * T) t, T/4 ≤ t ≤ 3T/4


However, I don't know if this is the correct input. I would appreciate it if anyone could tell me if my calculations are correct.

Thank you all very much.
 
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  • #2
I agree your algebra. However, your revised function isn't periodic; it's only defined on the range -T/4≤t<3T/4.

How can you modify the range to reflect the periodicity?
 

1. What is a periodic function?

A periodic function is a function that repeats its values at regular intervals. These intervals are called periods and are typically denoted by the variable T.

2. How are radians and time related in a periodic function?

In a periodic function, the independent variable is often represented in terms of radians, which is a unit of measurement for angles. Time and radians are related through the period T of the function. One complete cycle of the function corresponds to a period of T seconds.

3. Why is it necessary to convert a periodic function from radians to time?

Converting a periodic function from radians to time allows us to understand the function in terms of time, which is a more intuitive and familiar unit of measurement. It also makes it easier to analyze and compare different periodic functions.

4. How do you convert a periodic function from radians to time?

To convert a periodic function from radians to time, you can use the formula t = (r/2π)T, where t is the time in seconds, r is the angle in radians, and T is the period of the function in seconds.

5. Are there any limitations to converting a periodic function from radians to time?

Converting a periodic function from radians to time assumes that the function has a constant angular velocity. This may not be the case for all periodic functions, leading to inaccuracies in the conversion. Additionally, this conversion only applies to functions with a period of T seconds.

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