Question

an object moves in simple harmonic motion described by the equation d = 4 cos(π/2 t + π/2) where t is measured in seconds and d in inches. answer the following questions a through e about the equation. a what is the maximum displacement of the object?

Explanation:

Step1: Recall cosine - function range

The range of the cosine function $y = \cos(x)$ is $[- 1,1]$, i.e., $-1\leqslant\cos(x)\leqslant1$.

Step2: Analyze the given function

We have the function $d = 4\cos(\frac{\pi}{2}t+\frac{\pi}{2})$. Since $-1\leqslant\cos(\frac{\pi}{2}t+\frac{\pi}{2})\leqslant1$, to find the maximum value of $d$, we consider the maximum value of the cosine part. When $\cos(\frac{\pi}{2}t+\frac{\pi}{2}) = 1$, we calculate $d$.

Step3: Calculate the maximum value of $d$

Substitute $\cos(\frac{\pi}{2}t+\frac{\pi}{2}) = 1$ into the equation $d = 4\cos(\frac{\pi}{2}t+\frac{\pi}{2})$. Then $d=4\times1 = 4$.

Answer:

4 inches