Round answers to 2 decimal places.

a. Determine the position of the spring at

b. Find the velocity of t spring

Cheexorgeny
2021-12-14
Answered

A mass hanging from a vertical spring is in simple harmonic motion as given by the following position function, where t is measured in seconds and s is in inches: $s\left(t\right)=6\mathrm{cos}(\pi t+\frac{\pi}{4})$ .

Round answers to 2 decimal places.

a. Determine the position of the spring at$t=2.5s$

b. Find the velocity of t spring$t=2.5s$

Round answers to 2 decimal places.

a. Determine the position of the spring at

b. Find the velocity of t spring

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Mason Hall

Answered 2021-12-15
Author has **36** answers

Step 1

The given position function is:

where t is in seconds and

(a)

To determine

That is position at

So,

Terry Ray

Answered 2021-12-16
Author has **50** answers

Step 2

b)

Now velocity is given by:

$v\left(t\right)={s}^{\prime}\left(t\right)$

$=\frac{d}{dt}\left(s\left(t\right)\right)$

$=\frac{d}{dt}(-6\mathrm{cos}(\pi t+\frac{\pi}{4}))$

$=-6\frac{d}{dt}\left(\mathrm{cos}(\pi t+\frac{\pi}{4})\right)$

$=-6(-\mathrm{sin}(\pi t+\frac{\pi}{4})\times \pi )$

$=6\pi \mathrm{sin}(\pi t+\frac{\pi}{4})$

So,

$v\left(2.5\right)=6\pi \mathrm{sin}(\frac{5\pi}{2}+\frac{\pi}{4})$

$=6\pi \mathrm{sin}\left(\frac{11\pi}{4}\right)$

$\approx 13.33$

b)

Now velocity is given by:

So,

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