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?
-$$d = - 1 \cos \left( \frac { \pi } { 2 } t \right)$$
A) simple harmonic; $1 \mathrm {~m} ; \frac { 1 } { 4 }$ sec; 4 oscillations/sec
B) simple harmonic; $- 1 \mathrm {~m} ; 4 \mathrm { sec } ; \frac { 1 } { 4 }$ oscillation/sec
C) simple harmonic; $1 \mathrm {~m} ; 2 \mathrm { sec } ; \frac { 1 } { 2 }$ oscillation/sec
D) simple harmonic; $1 \mathrm {~m} ; 4 \mathrm { sec } ; \frac { 1 } { 4 }$ oscillation/sec

Question

Quizplus · Accepted Answer

The motion is simple harmonic with maximum displacement (amplitude) of 1 m. The period is $ \frac{2\pi}{\frac{\pi}{2}} = 4 $ seconds, and the frequency is $ \frac{1}{4} $ oscillation per second.

The Displacement D (In Meters) of an Object at Time d=−1cos⁡(π2t)d = - 1 \cos \left( \frac { \pi } { 2 } t \right)d=−1cos(2π​t)

The Displacement D (In Meters) of an Object at Time $d = - 1 \cos \left( \frac { \pi } { 2 } t \right)$