Solve the problem.
-Suppose that a weight on a spring has an initial position of $s ( 0 ) = - 5$ inches and a period of $P = 2.5$ seconds. Find a function $s ( t ) = a \cos ( 2 \pi F t )$ that models the displacement of the weight.
A) $\mathrm { s } ( \mathrm { t } ) = - 5 \cos ( 2 \pi ( 2.5 ) \mathrm { t } )$
B) $s ( t ) = - 10 \cos ( 2 \pi ( 2.5 ) t )$
C) $\mathrm { s } ( \mathrm { t } ) = - 5 \cos ( 2 \pi ( 0.4 ) \mathrm { t } )$
D) $s ( t ) = - 10 \cos ( 2 \pi ( 0.4 ) t )$

Question

Quizplus · Accepted Answer

The frequency $F$ is the reciprocal of the period $P$, so $F = \frac{1}{P} = \frac{1}{2.5} = 0.4$. The initial position $s(0) = -5$ inches indicates the amplitude $a = -5$. Therefore, the correct model is $s(t) = -5 \cos(2 \pi (0.4) t)$.

Solve the Problem s(0)=−5s ( 0 ) = - 5s(0)=−5 Inches and a Period Of

Solve the Problem $s ( 0 ) = - 5$ Inches and a Period Of