Question

The rod on a pump rises and falls as the pump operates. the following function gives the height of the top of the rod above the pumping unit in feet, l ⁡ ( t ) , as a function of time in seconds, t, after the pump is activated. l ⁡ ( t ) = 3 2 ⁢ sin ⁡ ( π ⁢ t π 2 ) 3 2 what is the period of the given function? 1 second 2 seconds 4 seconds 3 seconds

Answer 1

The period of the function representing the height of the rod in the pump is 2 seconds, as determined from the coefficient of the time variable in the sine function of the given equation.

Step-by-step explanation:

The student has given the function l(t) = ½ sin(π t + π/2) ½, which describes the motion of the rod on a pump as a function of time. To find the period of this function, we can look at the coefficient of t inside the sine function. The standard form of a sine function is sin(ω t + φ), where ω is the angular frequency and T, the period, is given by T = 2π/ω. In this case, our ω is equal to π, so the period T can be calculated as T = 2π/π = 2 seconds. Therefore, the correct answer is that the period of the given function is 2 seconds.