A mass hanging from a vertical spring is in simple harmonic

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(t)=6cos(πt+π4).
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
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Expert Answer

Mason Hall
Answered 2021-12-15 Author has 36 answers

Step 1
The given position function is:
s(t)=6cos(πt+π4)
where t is in seconds and s(t) is in inches.
(a)
To determine s(2.5).
That is position at t=2.5
So,
s(2.5)=6cos(π(2.5)+π4)
=6cos(5π2+π4)
=6cos(11π4)
4.24

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Terry Ray
Answered 2021-12-16 Author has 50 answers
Step 2
b)
Now velocity is given by:
v(t)=s(t)
=ddt(s(t))
=ddt(6cos(πt+π4))
=6ddt(cos(πt+π4))
=6(sin(πt+π4)×π)
=6πsin(πt+π4)
So,
v(2.5)=6πsin(5π2+π4)
=6πsin(11π4)
13.33
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