Find a function that models simple harmonic motion having the given properties. Assume that the displacement is zero at time $t = 0$ .amplitude 10 m, frequency $2.0 \mathrm {~Hz}$
A) $y = 4 \sin 10 \pi t$
B) $y = 10 \sin 4 t$
C) $y = 2 \sin 4 \pi t$
D) $y = 10 \sin 4 \pi t$
E) $y = 5 \sin 4 \pi t$

Question

Quizplus · Accepted Answer

Simple harmonic motion is modeled by the equation $y = A \sin (\omega t)$, where $A$ is the amplitude and $\omega$ is the angular frequency, related to the frequency $f$ by $\omega = 2\pi f$. 
Using this equation and the given values, we get $y = 10\sin(2\pi(2)t) = 10\sin(4\pi t)$. Therefore, the correct choice is D.

Find a Function That Models Simple Harmonic Motion Having the Given