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 general form of a sine function is $y = A\sin(Bx + C)+D$. For the function $y=\sin(x)$, the range is $[- 1,1]$. In the given displacement function $d = 0.4\sin(1760\pi t)$, the amplitude is $A = 0.4$.

Step2: Determine maximum value

The maximum value of the sine function $\sin(1760\pi t)$ is 1. When $\sin(1760\pi t)=1$, the displacement $d$ reaches its maximum value. Substitute $\sin(1760\pi t) = 1$ into the equation $d = 0.4\sin(1760\pi t)$. Then $d=0.4\times1$.

Answer:

$0.4$ mm