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; $6 \mathrm {~m} ; \frac { 2 } { 5 } \pi \mathrm { sec } ; \frac { 5 } { 2 \pi }$ oscillations/sec
D) simple harmonic; $6 \mathrm {~m} ; 5 \pi \mathrm { sec } ; \frac { 5 } { \pi }$ oscillations/sec

Question

Quizplus · Accepted Answer

The equation $d = 6 \sin ( 5 t )$ describes simple harmonic motion with a maximum displacement (amplitude) of 6 meters from the resting position. The angular frequency $\omega$ is 5 rad/s, which gives a period $T = \frac{2\pi}{\omega} = \frac{2\pi}{5}$ seconds for one complete oscillation. The frequency $f = \frac{1}{T} = \frac{5}{2\pi}$ oscillations per second.

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 $d = 6 \sin ( 5 t )$