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Yuliya22 [10]
3 years ago
14

If a spring is oscillating (moving) according to the velocity equation v(t) = 2sin(t) (in ft/s), then what is its displacement o

ver its first π seconds of travel?
Mathematics
1 answer:
Feliz [49]3 years ago
7 0

ANSWER

4 ft

EXPLANATION

The velocity equation of the oscillating spring is given by the function.

v(t)=2  \sin(t)   \:  \:  {ms}^{ - 1}

To find the displacement function, we need to to Integrate the velocity function.

s(t) = \int \: 2 \sin(t) dt

s(t) =  -  2 \cos(t)  + k

At time t=0, there was no displacement.

This implies that,

s(0) = 0

0=  -  2 \cos(0)  + k

0=  -  2 + k

k = 2

The displacement function then becomes,

s(t) =  -  2 \cos(t)  + 2

To find the displacement over the first π seconds, we put

t = \pi

into the equation for the displacement to get,

s(\pi) =  -  2 \cos(\pi)  + 2

s(\pi) =  -  2 ( - 1)  + 2

s(\pi) =  2  + 2 =4 ft

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