Question

Please help me! Problem is attached

Answer 1

Whatever you do, don't just give me the answer. if you could explain how you would do it I would appreciate it

Answer 2

At t = Pi/8, you just substitute t into y(t) then you have the answer

\[y(\pi/8) = \frac{ \cos(12 \pi/8) }{ 3 } - \frac{ \sin (12\pi/8) }{ 4 } = \frac{ \cos(3 \pi/2) }{ 3 } - \frac{ \sin (3\pi/2) }{ 4 } \]
\[ = 0 - \frac{ -1 }{ 4 } = \frac{ 1 }{ 4 } feet\]
Velocity of object is derivative of distance function over time

\[v(t) = \frac{ dy(t) }{ dt } = \frac{ \frac{ 1 }{ 3 } dcos12t }{ dt } - \frac{ \frac{ 1 }{ 4 } dsin12t }{ dt }\]
\[= \frac{ 1 }{ 3 } \frac{ \sin12t }{ 12 } - \frac{ 1 }{ 4 } \frac{ -\cos12t }{ 12 } = \frac{ \sin12t }{ 36 }+\frac{ \cos12t }{ 48 }\]

Again, try to substitute t = pi/8 into v(t) then calculate by yourself

Answer 3

One note is that if v(t) takes the negative value, don't worry. Because the object is moving the opposite direction to the spring at that time

Answer 4

So the position is 1/4 feet?

Answer 5

Yes, is it clear to you already? if not understand then ask again

Answer 6

So then the velocity is sin12 t /36+cos12 t /48

Answer 7

and I plug pi/8 in for t to find the velocity?

Answer 8

Yes, and take a look at my second answer of note about velocity v(t) then you may not be surprised.

Answer 9

Im confused on what cos3pi/2 /48 is

Answer 10

Do you know what cos pi/2 is ? don't care about 48