Solve Pendulum Problem: Find Position in 1.6 Sec

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In summary, Daniel found that the amplitude(A) is 0.017 meter and that the argument of cosine is about 4.6 degrees.
  • #1
beanryu
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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!
 
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  • #2
the amplitude(A) is in dimension of degree, not meter... tell me where is your .0017 m came from ? ...
 
  • #3
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.
 
  • #4
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
 
  • #5
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...
 
  • #6
okay, thank you vincentchan.
 

What is the pendulum problem and how is it solved?

The pendulum problem refers to finding the position of a pendulum at a specific time, given its initial conditions. It can be solved using the equation of motion for a simple pendulum, which takes into account the length of the pendulum, the gravitational constant, and the initial angle and velocity of the pendulum.

What is the significance of finding the position of a pendulum in 1.6 seconds?

In physics, the time it takes for a pendulum to complete one full swing is known as the period. The period of a pendulum is dependent on its length and the gravitational constant. Finding the position of a pendulum in 1.6 seconds can help determine its period and other important characteristics, such as its frequency and energy.

What are the initial conditions needed to solve the pendulum problem?

To solve the pendulum problem, the initial conditions required are the length of the pendulum, the gravitational constant, the initial angle of the pendulum (measured from the vertical), and the initial velocity of the pendulum (if present). These values can be measured or given in the problem statement.

Is the solution to the pendulum problem affected by air resistance?

The simple pendulum equation assumes that there is no air resistance, so in theory, the solution should not be affected by air resistance. However, in real-world scenarios, air resistance can have a small impact on the motion of the pendulum, especially for longer and heavier pendulums.

What are some practical applications of solving the pendulum problem?

The pendulum problem has various practical applications, such as in timekeeping devices like grandfather clocks and metronomes. It is also used in seismology to measure the motion of the Earth's crust during an earthquake. Additionally, pendulums are used in various scientific experiments to study the principles of oscillation and energy conservation.

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