Find a model for simple harmonic motion satisfying the specified conditions. ?
Displacement (t = 0): 0
Amplitude: 5 meters
Period: 10 seconds
?
A) $d = 5 \sin \left( \frac { \pi t } { 5 } \right)$ ?
B) $d = 5 \sin ( 2 \pi t )$ ?
C)? $d = 5 \sin \left( \frac { \pi t } { 12 } \right)$ ?
D) $d = 10 \sin ( \pi t )$ ?
E) $d = 5 \cos ( 2 \pi t )$ ?

Question

Quizplus · Accepted Answer

The correct model is $d = 5 \sin \left( \frac { \pi t } { 5 } \right)$ because it starts at 0 (satisfying the initial displacement condition), has an amplitude of 5, and a period of $10$ seconds, which matches the given conditions. The period $T$ of a sine function in the form $d = A \sin(Bt)$ is given by $T = \frac{2\pi}{B}$, so setting $T = 10$ gives $B = \frac{\pi}{5}$.

Find a Model for Simple Harmonic Motion Satisfying the Specified d=5sin⁡(πt5)d = 5 \sin \left( \frac { \pi t } { 5 } \right)d=5sin(5πt​)

Find a Model for Simple Harmonic Motion Satisfying the Specified $d = 5 \sin \left( \frac { \pi t } { 5 } \right)$