The function $y = 1.6 \sin ( t - 1.8 )$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find the frequency of motion
A) $\frac { 1 } { 2 \pi } \text { cycles per second }$
B) $1.6 \text { cycles per second }$
C) $1.8 \text { cycles per second }$
D) $2 \pi \text { cycles per second }$
E) $3.9 \text { cycles per second }$

Question

Quizplus · Accepted Answer

The frequency of a sinusoidal function like $y = 1.6 \sin(t - 1.8)$ is determined by the coefficient of $t$ inside the sine function, which in this case is 1 (since it's simply $t$ without a coefficient in front of it). The general form is $y = A \sin(B(t - C)) + D$, where $B = 2\pi \times \text{frequency}$. Since $B = 1$ here, the frequency is $\frac{1}{2\pi}$ cycles per second.

The Function y=1.6sin⁡(t−1.8)y = 1.6 \sin ( t - 1.8 )y=1.6sin(t−1.8)

The Function $y = 1.6 \sin ( t - 1.8 )$