Solve the problem.
-Write the equations that describe the simple harmonic motion of a particle moving uniformly around a circle of radius 7 units, with linear speed 5 units per second.
A) $x = 7 \cos 5 t , y = 7 \sin 5 t$
B) $x = 5 \cos 7 t , y = 7 \sin 5 t$
C) $x = \cos 7 t + 5 , y = \sin 7 t + 5$
D) $x = 7 \sin 5 t , y = 7 \sin 5 t$

Question

Quizplus · Accepted Answer

The equations for a particle moving in simple harmonic motion around a circle of radius $r$ with a linear speed $v$ are given by $x = r \cos(\omega t)$ and $y = r \sin(\omega t)$, where $\omega$ is the angular speed. Since the radius is 7 units and the linear speed is 5 units per second, and assuming the linear speed $v = \omega r$ leads to $\omega = \frac{v}{r} = 5$, the correct equations are $x = 7 \cos(5t)$ and $y = 7 \sin(5t)$, which matches choice A.

Solve the Problem x=7cos⁡5t,y=7sin⁡5tx = 7 \cos 5 t , y = 7 \sin 5 tx=7cos5t,y=7sin5t

Solve the Problem $x = 7 \cos 5 t , y = 7 \sin 5 t$