Find a model for simple harmonic motion satisfying the specified conditions.
Displacement (t = 0): 0
Amplitude: 5 centimeters
Period: 2 seconds

A) $d = 5 \cos ( 2 \pi t )$
B) $d = 5 \sin \left( \frac { \pi t } { 2 } \right)$
C) $d = 5 \sin ( \pi \mathrm { t } )$
D) $d = 2 \sin ( \pi t )$
E) $d = 5 \sin ( 2 \pi t )$

Question

Find a model for simple harmonic motion satisfying the specified conditions.  
Displacement (t = 0): 0
Amplitude: 5 centimeters
Period: 2 seconds
 
A) $d = 5 \cos ( 2 \pi t )$
B)  $d = 5 \sin \left( \frac { \pi t } { 2 } \right)$
C) $d = 5 \sin ( \pi \mathrm { t } )$  
D) $d = 2 \sin ( \pi t )$  
E) $d = 5 \sin ( 2 \pi t )$

Quizplus · Accepted Answer

The displacement is zero at $t = 0$, which matches the sine function. The amplitude is 5, and the period is 2 seconds, which corresponds to the function $d = 5 \sin (\pi t)$.

Find a Model for Simple Harmonic Motion Satisfying the Specified d=5cos⁡(2πt)d = 5 \cos ( 2 \pi t )d=5cos(2πt)

Find a Model for Simple Harmonic Motion Satisfying the Specified $d = 5 \cos ( 2 \pi t )$