An object undergoing simple harmonic motion in the x-direction has a period of 2.0 seconds,an amplitude of 5 cm and begins its oscillation at t = 0 at its maximum value of x.What equation could describe its motion?
A)x(t)= 0.05 sin (2.0t + $\pi$/4)
B)x(t)= 0.05 cos(2.0t + $\pi$/4)
C)x(t)= 0.05 sin($\pi$t - $\pi$/4)
D)x(t)= 0.05 cos($\pi$t)
E)x(t)= 0.05 cos($\pi$t - $\pi$/4)

Question

Quizplus · Accepted Answer

The correct equation for an object undergoing simple harmonic motion, starting at its maximum displacement (amplitude) at t = 0, is given by $x(t) = A \cos(\omega t + \phi)$, where $A$ is the amplitude, $\omega$ is the angular frequency, and $\phi$ is the phase constant. Since the object starts at its maximum value, a cosine function is appropriate, and there's no need for a phase shift ($\phi = 0$). The amplitude is 5 cm (or 0.05 m), and the period $T = 2.0$ seconds, which relates to the angular frequency $\omega$ by $\omega = \frac{2\pi}{T}$. Thus, the equation with a cosine function, correct amplitude, and angular frequency derived from the given period without an additional phase shift is the correct choice.

An Object Undergoing Simple Harmonic Motion in the X-Direction Has π\piπ

An Object Undergoing Simple Harmonic Motion in the X-Direction Has $\pi$