For the simple harmonic motion described by the trigonometric function, find the frequency per second. $d = \frac { 1 } { 4 } \sin 6 \pi t$
A) $3$
B) $6$
C) $3 \pi$
D) $6 \pi$
E) $2 \pi$

Question

For the simple harmonic motion described by the trigonometric function, find the frequency per second.   $d = \frac { 1 } { 4 } \sin 6 \pi t$  
A) $3$
B) $6$
C) $3 \pi$
D) $6 \pi$
E) $2 \pi$

Quizplus · Accepted Answer

The frequency of a trigonometric function in simple harmonic motion is given by the coefficient of $t$ in the argument of the sine or cosine function. In the given function $d = \frac{1}{4} \sin 6\pi t$, the coefficient of $t$ is $6\pi$. The frequency $f$ is related to the angular frequency $\omega$ by the formula $\omega = 2\pi f$. Given that $\omega = 6\pi$, we can solve for $f$ as follows: $6\pi = 2\pi f$, which simplifies to $f = 3$. Therefore, the frequency is 3 Hz.

For the Simple Harmonic Motion Described by the Trigonometric Function d=14sin⁡6πtd = \frac { 1 } { 4 } \sin 6 \pi td=41​sin6πt

For the Simple Harmonic Motion Described by the Trigonometric Function $d = \frac { 1 } { 4 } \sin 6 \pi t$