Answer :
Answer:
The position and velocity of the spring is −2.12 inches and -6.66 ft/s.
Explanation:
Given that,
The position function,
[tex]s(t)=-3\cos(\pi t+\dfrac{\pi}{4})[/tex]
We need to calculate the position of the spring at t = 1.5 s
Using position function
[tex]s(t)=-3\cos(\pi t+\dfrac{\pi}{4})[/tex]
Put the value of t in the function
[tex]s(1.5)=-3\cos(\pi\times1.5+\dfrac{\pi}{4})[/tex]
[tex]s(1.5)=-2.12\ inches[/tex]
We need to calculate the velocity of the spring
Using position function
[tex]s(t)=-3\cos(\pi t+\dfrac{\pi}{4})[/tex]
On differentiating
[tex]\dfrac{ds}{dt}=3\pi\sin(\pi t+\dfrac{\pi}{4})[/tex]
[tex]v(t)=3\pi\sin(\pi t+\dfrac{\pi}{4})[/tex]
Put the value into the formula
[tex]v(1.5)=3\pi\sin(1.5\pi+\dfrac{\pi}{4})[/tex]
[tex]v(1.5)=-6.66\ ft/sec[/tex]
Hence, The position and velocity of the spring is −2.12 inches and -6.66 ft/s.