Question

the displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.4sin(1760πt). what is the maximum displacement of the tuning fork?
0.2 mm
0.4 mm
0.8 mm
2.5 mm

Explanation:

Step1: Recall sine - function property

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

Step2: Analyze the given function

We have the displacement function $d = 0.4\sin(1760t)$. Since the maximum value of $\sin(1760t)$ is $1$.

Step3: Calculate the maximum displacement

When $\sin(1760t)=1$, $d = 0.4\times1=0.4$ mm.

Answer:

0.4 mm