Simple Harmonic Motion - seemingly easy yet

AI Thread Summary
The discussion centers on calculating the displacement of a body in simple harmonic motion using the equation x = (2.0 m) cos[(2pi rad/s)t + pi/2 rad] at t = 4.0 s. The initial poster mistakenly calculated the cosine value without properly accounting for the periodic nature of the trigonometric function, leading to confusion about the expected result. It was clarified that plugging in t = 4 results in an angle of pi/2 radians, where the cosine value is zero. The poster's calculator output of 6E^-13 was acknowledged as effectively zero, confirming the misunderstanding. Ultimately, the importance of recognizing the periodic properties of trigonometric functions in such calculations was emphasized.
Shadow Cloud
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The function x = (2.0 m) cos[(2pi rad/s)t + pi/2 rad] gives the simple harmonic motion of a body. Find the following values at t = 4.0 s.
(a) the displacement: ____m
Correct me if I am wrong, but to get x all I have to do is just plug 4.0 s in for t in that equation mentioned above right? I set my calculator to radians and did what I just said and get 6E^-13, but for some reason webassign (website where I answer the problem at) says I'm wrong. What gives?
 
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Shadow Cloud said:
Correct me if I am wrong, but to get x all I have to do is just plug 4.0 s in for t in that equation mentioned above right?
That's all there is to it.
I set my calculator to radians and did what I just said and get 6E^-13, but for some reason webassign (website where I answer the problem at) says I'm wrong.
You made a mistake. What angle (in radians) are you taking the cosine of?
 
Oh I'm sorry, I forgot to include the pi in the equation.
 
So I assume you corrected your mistake?
 
Oh I haven't, I just forgot to include it when I posted the problem. I still do not understand why I am not getting the right answer when all I have to do is plug in 4.0 for T.
 
I think if you just take a look at the trigonometric function itself, it should be no surprise to you that any integer value of t will result in the cosine function returning 0.
 
Shadow Cloud said:
I still do not understand why I am not getting the right answer when all I have to do is plug in 4.0 for T.
mezarashi explained it, but your real mistake is using a calculator to solve this. :smile: If you just looked at the equation, you'd see that plugging in T = 4 sec gives you an angle of pi/2 radians. What's the cosine of pi/2 radians (or 90 degrees)? (Note that 8 1/2 pi radians is equivalent to pi/2 radians since the trig functions are periodic over 2 pi radians.)

Your calculator answer was "correct": 6E^-13 is pretty close to zero! (Round it off.)
 
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And pi/2 for cos is 0...yes you're right, the calculator did mess me up in this case. Thank you for the help.
 
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