Board the Boat When It's Within 10cm of the Dock

[Ronnin]

A boat(1500kg) is on a lake exibiting SHM with an amp of 20cm bobbing on the waves. The boat takes 3.5s to make one complete up and down cycle. When the boat is at its highest point it is at the same level as the dock. You will only board the boat if it is within 10cm of the dock. How much time do you have to board the boat per cycle.

Can someone give me a hint on how to start with this problem. I know I'm looking for the interval in the sine wave where f(x) is greater than 10cm. Any ideas?

 

[Hootenanny]

Do you know the general expression for representing the vertical displacement of SHM?

 

[Ronnin]

it it x(t)=Asin(omega*t+delta)? Am I thinking about the right formula?

 

[radou]

it it x(t)=Asin(omega*t+delta)? Am I thinking about the right formula?

Yes, you are. It would be more appropriate to call it y(t) in this case, but it doesn't really mater.

 

[Ronnin]

Still need a little help. Not quite sure how the math is supposed to work in this one.

 

[Hootenanny]

Okay so your looking for the time interval of t when y(t)>0.1; so the first thing we need to do is find when y(t)=0.1,

$$A\sin\left(\omega \cdot t)=0.1$$

Now, can you solve for t?

Edit: It may also be useful to restrict our domain here to something like;

$$dom\left[ 0,\frac{1}{f} \right]$$

So that we only consider one time period.

 

[Ronnin]

Sorry Hoot, that's the part I don't remember. I'm rusty on the how the trig works here. Can I just take the sin inverse for each side of the equation?

 

[Hootenanny]

Sorry Hoot, that's the part I don't remember. I'm rusty on the how the trig works here. Can I just take the sin inverse for each side of the equation?

Yes, sounds good to me, although I would divide through by A beforehand. Also take note of the edit in my above post.