If a spring is oscillating (moving) according to the velocity equation v(t) = 2sin(t) (in ft/s), then what is its displacement over its first π seconds of travel?

ANSWER

4 ft

EXPLANATION

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

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

At time t=0, there was no displacement.

This implies that,

The displacement function then becomes,

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

into the equation for the displacement to get,

77

step-by-step explanation: