the displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled…

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?\n0.2 mm\n0.4 mm\n0.8 mm\n2.5 mm

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?\n0.2 mm\n0.4 mm\n0.8 mm\n2.5 mm

Answer

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 function $d = 0.4\sin(1760\pi t)$. Since $-1\leqslant\sin(1760\pi t)\leqslant1$, when $\sin(1760\pi t)=1$, the displacement $d$ reaches its maximum value.

Step3: Calculate the maximum displacement

Substitute $\sin(1760\pi t) = 1$ into the equation $d = 0.4\sin(1760\pi t)$. We get $d_{max}=0.4\times1 = 0.4$ mm.

Answer:

B. 0.4 mm