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

Quizplus · Accepted Answer

The equation for simple harmonic motion is given by:
x = A cos(2πt/T)
where x is the displacement, A is the amplitude, t is the time, and T is the period.
Given that the displacement at t=0 is 0 and the amplitude is 5 centimeters, we know that:
x = 5 cos(2πt/T)
To find T, we know that the period is 2 seconds, so:
2 = T
Substituting this value into the equation gives us:
x = 5 cos(πt)
Therefore, the best choice is C, which corresponds to the graph of y = cos(x).

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 $d = 5 \cos ( 2 \pi t )$