Solve Pendulum Problem: Find Position in 1.6 Sec

[beanryu]

I got a SHM problem:

a pendulum is released 15 degrees from the vertical and has a frequency of 2, what is its position in 1.6 sec. Hint: (don't confuse the swing angle with the argument of cosine)

I found that the amplitude(A) is an arc of about 0.017m.

I used the equation: X = A cos ( 2 "pie" f t )
but my answer is wrong. I got X=0.016 and it represent an angle of about 0.88 degrees. But according to the book, it should be 4.6 degrees away from the equilibrium point.

In addition, can someone tell me what does the "argument of cosine" mean?

Thank you for replying!

 

[vincentchan]

the amplitude(A) is in dimension of degree, not meter... tell me where is your .0017 m came from ? ...

 

[dextercioby]

The problem is wrongly formulated...For an amplitude of oscillation if 15°,the linear approximation will not hold...In this case the solution is expressible through Jacobi's elliptic functions...

Daniel.

 

[beanryu]

T = 1/f

T = 2 "pie" square root of (L/g)

I got L is about 0.06 meter, which is the length of the string where the weight is hanging.
I calculated the circumference using C = 2 "pie" r, where I used the value of L as the value of the radius, and got the result of about 0.38 meter.
Then I used the following ration : (x/0.38)=(15degrees/360degrees) and found x to be an arc that covers the amplitude in about 0.017 meter.

I think my way is kind of long and maybe there's another short way to finger it out, but this is how I did it, and can anyone provide further suggestion or advices?

Maybe you are right, Dextercioby, the textbook said its about 15 degrees.

Thank you

 

[vincentchan]

the exact solution for a large angle is not easy.. and not for your level... forget it...
since the arc length is directly proportional to the angle (hope you can see that). It is meaningless to find the arclength. you equation X=Acos(2pi f t) works as well as angle or the arc length. put A = 15 degree, X will be your answer...

 

[beanryu]

okay, thank you vincentchan.