Alrighty I have to find two real world sinusoidal functions. I found:
1. A piston in an engine moves up and down in a cylinder. The height, h centimeters, of the piston a t seconds is given by the function: h= 120 sin(πt) + 200.
2. You can find the amplitude of a wave with the function: v(t) = Ec sin wct + Ɵ
but I am having a hard time grasping how exactly to answer the following questions about each.. ?
ANY help would be greatly appreciated.
1.What aspect of the natural phenomenon involves data that repeats after a given period of time?
2. How could you use the equation to solve problems?
1. The aspect of the natural phenomenon that involves data that repeats after a given period of time is called periodicity. In the first function you mentioned, the piston in an engine moves up and down in a repetitive manner. The height of the piston, represented by the function h(t), repeats after a certain time period. In this case, the period is determined by the value of π, which is approximately 3.14159.
2. Solving problems using the given equations involves various aspects. Let's break it down for each function:
For the first function h(t) = 120 sin(πt) + 200, some possible problem-solving applications could include:
- Determining the height of the piston at a specific time (t).
- Finding the time it takes for the piston to reach a specific height.
- Analyzing the maximum and minimum heights of the piston.
To solve these problems, you would substitute the given values into the equation and solve for the unknown variable. For example, if you want to find the height of the piston at t = 2 seconds, you would substitute t = 2 into the equation h(t) = 120 sin(πt) + 200 and calculate the result.
For the second function v(t) = Ec sin(wct) + Ɵ, the equation relates to the amplitude of a wave. Some possible problem-solving applications could include:
- Determining the amplitude of a wave given the values of Ec (Amplitude scaling factor) and Ɵ (phase shift).
- Analyzing the effect of changing the values of Ec and Ɵ on the wave.
To solve problems using this equation, you would substitute the given values of Ec, Ɵ, and other relevant variables into the equation, and calculate the amplitude of the wave.
In both cases, it's essential to understand the variables and constants in the equations, as well as how they relate to the real-world phenomenon you are studying. By substituting appropriate values, you can use the equations to find specific information and solve problems related to the given phenomenon.