mrcrazyog Posted March 30, 2013 Report Share Posted March 30, 2013 (edited) Hey guys, I would really appreciate any kind of help with this problem: "A spring is suspended from the ceiling. It is pulled down and released, and then oscillates up and down. Its length, l centimetres, is modelled by the function l = 33 + 5cos((720t)°), where t is time in seconds after release." I got stuck at c, where it asks me to find the first time at which the length is 33 cm. Of course I could do it using my GDC, but according to the markscheme, there should be a much easier way to solve this. Unfortunately, even though I have the results with me I just can't see why it is the way it is... What the MS says is to set up an equation 33 = 33 + 5cos 720t, which gives me 0 = 5cos 720t. OK, I got that one. But now it says: 720t = 90, and thus it follows that t = 1/8... What I don't get is HOW the heck they got the 90... Any idea? Thanks so much! Edited March 30, 2013 by mrcrazyog Reply Link to post Share on other sites More sharing options...
Meat Posted March 30, 2013 Report Share Posted March 30, 2013 For the first time at which the length is 33, they want you to find the smallest positive value for t so that 5cos(720t)=0. We know that for cos(x) the smallest positive value of x for cos(x) to equal 0 is 90, so you equate 720t to 90 and solve for t.Actually, there is an infinite amount of values of t for 5cos(720t) to equal 0, but they only want the smallest positive value; smallest because the question says the first time at which the length is 33, and positive because we are dealing with time.If you need more clarification I won't mind helping more Reply Link to post Share on other sites More sharing options...
mrcrazyog Posted March 30, 2013 Author Report Share Posted March 30, 2013 Thanks, I figured the thing about 90, too, but what I don't get now is why they got rid of the 5cos completely after getting the 90. What I would do is just substitute 90 like this: 5cos 720t = 90. But why do they use only 720t = 90 and omit the cosine completely? Reply Link to post Share on other sites More sharing options...
Meat Posted March 30, 2013 Report Share Posted March 30, 2013 Because we want 5cos(720t) = 0 so that l = 33For cos of anything to equal 0, the angle inside the cos is what should be 90 (or 270, 450, etc. but this is irrelevant in this case). 720t is the angle, so we need that to = 90, we need the whole cosine function to = 0. Also, remember that cos of any number should be between -1 and 1, inclusive, so 5cos(720t)=90 isn't even possible. Reply Link to post Share on other sites More sharing options...
mrcrazyog Posted March 30, 2013 Author Report Share Posted March 30, 2013 Oh, OK - so the whole thing inside the cos function has to equal the angle. Now I get it Thanks so much Reply Link to post Share on other sites More sharing options...
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