Question

I have gotten y=(1.75)*cos(pi*x/14)
Is this result correct?
http://prntscr.com/d3mbns

Answer 1

@mathmate
If you could help, I would be grateful!

Answer 2

Yep, we'll look at the question carefully.
Simple Harmonic motion means it's either sine or cosine, agree?

Answer 3

The other key points are :
the motion has it's high point at t=0, so using cosine is good.
It also says "it \(returns\) to its high point every 14 seconds, which means that the period is 14 seconds (from high to high).

Answer 4

I have calculated the \[\Large\color{purple}{\text{amplitude}}=\frac{ 3.5 }{ 2 }=\frac{ 7 }{ 4 }=1.75\]

and the \[\Large\color{lightgreen}{\text{amplitude}}=\frac{ 2\pi }{ 2*14 }=\frac{ \pi }{ 14 }\]

and mentioned that the top\maximum point occurred at \[\huge\color{red}{t=0}\]
that means it is a cosine function!

That is what I think...

Answer 5

Sorry
\[\Large\color{lightgreen}{\text{period}}=\frac{ 2\pi }{ 2*14 }=\frac{ \pi }{ 14 }\]

Answer 6

Well, most of your answer is correct, BUT

you wrote 2*14 at the bottom, but since it is high to high, which is a complete period in 14 seconds, so T=14, or the argument for cosine is just (2pi t)/14.

The question does not specify the origin of y, but from the diagram, it seems that y=0 at the equilibrium position is fine, so the above is the only change you need.

Answer 7

http://prnt.sc/d3mh7q

Answer 8

I got what you explained!

Thank you very much for your good explanation.

The equation would be like that:
\[\huge y(x)=\frac{ 7 }{ 4 }\cos(\frac{ \pi }{ 7 }x)\]

Answer 9

Yes, I would not hesitate to write
(7/4)cos(2pi x /14) to underline that the period is 14, with an amplitude of 7/4. but not sure if the computer is smart enough to interpret it correctly.