The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the
maximum displacement from its resting position, the time required for one oscillation, and the frequency?
-$$d = 6 \sin ( 5 t )$$
A) simple harmonic; $- 6 \mathrm {~m} ; \frac { 2 } { 5 } \pi \mathrm { sec } ; \frac { 5 } { 2 \pi }$ oscillations/sec
B) simple harmonic; $6 \mathrm {~m} ; \frac { 5 } { 2 \pi } \mathrm { sec } ; \frac { 2 } { 5 } \pi$ oscillations/sec
C) simple harmonic; $6 \mathrm {~m} ; \frac { 2 } { 5 } \pi$ sec; $\frac { 5 } { 2 \pi }$ oscillations/sec
D) simple harmonic; $6 \mathrm {~m} ; 5 \pi \mathrm { sec } ; \frac { 5 } { \pi }$ oscillations/sec

Question

Quizplus · Accepted Answer

The motion is simple harmonic because it follows the sine function. The maximum displacement (amplitude) is the coefficient of sine, which is $6 \, \text{m}$. The time for one oscillation (period) is given by $T = \frac{2\pi}{\omega}$, where $\omega = 5$, so $T = \frac{2\pi}{5}$ sec. The frequency $f = \frac{1}{T} = \frac{5}{2\pi}$ oscillations/sec.

The Displacement D (In Meters) of an Object at Time d=6sin⁡(5t)d = 6 \sin ( 5 t )d=6sin(5t)

The Displacement D (In Meters) of an Object at Time $d = 6 \sin ( 5 t )$