use the drawing tool to form the correct answers on the provided graph.\na student observes that the motion…

use the drawing tool to form the correct answers on the provided graph.\na student observes that the motion of a weight oscillating up and down on a spring can be modeled by this equation, where (h(t)) is the weights height above the ground, in meters, and (t) is the time, in seconds.\n(h(t)=0.5sin(pi t+\frac{pi}{2}) + 1)\non the graph, plot the points where height, (h(t)), is at a maximum.

use the drawing tool to form the correct answers on the provided graph.\na student observes that the motion of a weight oscillating up and down on a spring can be modeled by this equation, where (h(t)) is the weights height above the ground, in meters, and (t) is the time, in seconds.\n(h(t)=0.5sin(pi t+\frac{pi}{2}) + 1)\non the graph, plot the points where height, (h(t)), is at a maximum.

Answer

Answer:

The maximum value of (h(t)) occurs when (\sin(\pi t+\frac{\pi}{2}) = 1). The points to be plotted are ((0, 1.5),(2, 1.5),(4, 1.5),(6, 1.5)\cdots) (in general, for (t = 2n), (n = 0,1,2,\cdots), (h(t)=1.5))

Explanation:

Step1: Recall sine - function property

The maximum value of the sine function (y = \sin(x)) is (y = 1).

Step2: Set the argument of sine equal to the value for maximum

We set (\pi t+\frac{\pi}{2}=\frac{\pi}{2}+ 2k\pi), (k\in\mathbb{Z}).

Step3: Solve for (t)

Subtract (\frac{\pi}{2}) from both sides of (\pi t+\frac{\pi}{2}=\frac{\pi}{2}+ 2k\pi). We get (\pi t=2k\pi), then (t = 2k), (k = 0,1,2,\cdots).

Step4: Find the maximum value of (h(t))

Substitute (\sin(\pi t+\frac{\pi}{2}) = 1) into (h(t)=0.5\sin(\pi t+\frac{\pi}{2})+1). Then (h(t)=0.5\times1 + 1=1.5).