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

Step2: Determine the maximum value of the displacement

When $\sin(1760\pi t)=1$, the displacement $d$ reaches its maximum value. Since $d = 0.4\sin(1760\pi t)$, substituting $\sin(1760\pi t)=1$ into the equation, we get $d_{max}=0.4\times1 = 0.4$ mm.

Answer:

0.4 mm