Question

A mass hanging from a spring is set in motion and its ensuing velocity is given by $v(t) = 2pi cos pi t$, for $t ge 0$. Assume that the positive direction is upward and $s(0) = 0$. (a) Determine the position function, for $t ge 0$. (b) Graph the position function on the interval $[0, 4]$. (c) At what times does the mass reach its low point the first three times? (d) At what times does the mass reach its high point the first three times?

          A mass hanging from a spring is set in motion and its ensuing velocity is given
by $v(t) = 2pi cos pi t$, for $t ge 0$. Assume that the positive direction is upward and
$s(0) = 0$.
(a) Determine the position function, for $t ge 0$.
(b) Graph the position function on the interval $[0, 4]$.
(c) At what times does the mass reach its low point the first three times?
(d) At what times does the mass reach its high point the first three times?

A mass hanging from a spring is set in motion and its ensuing velocity is given
by v(t) = 2pi cos pi t, for t ge 0. Assume that the positive direction is upward and
s(0) = 0.
(a) Determine the position function, for t ge 0.
(b) Graph the position function on the interval [0, 4].
(c) At what times does the mass reach its low point the first three times?
(d) At what times does the mass reach its high point the first three times?

Added by Robert H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Carson Merrill

06/03/2023

Step 1

We have: v(t) = ds/dt = 21 cos #t Integrating both sides with respect to t, we get: s(t) = ∫v(t)dt = ∫21 cos #t dt = 21 sin #t / # where # is a constant representing the frequency of the motion. Since s(0) = 0, we have: s(t) = 21 sin #t / # (b) To graph the Show more…

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