Simple Harmonic Motion , finding the time taken to travel an angular dispalcemnt

AI Thread Summary
To find the time taken for a pendulum to reach half its maximum angular displacement, the maximum angular displacement was calculated as 68.8 degrees, leading to a half displacement of 34.4 degrees. The angular velocity was derived using the formula sqrt(g/l), where g is 9.8 m/s² and l is 6 m. The initial attempt to divide the angular displacement by angular velocity yielded an incorrect result. Participants suggested expressing angular displacement as a function of time, indicating the involvement of a trigonometric function for the solution. The correct answer, as referenced in the textbook, is 4.1 seconds.
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1. Homework Statement

Find the time taken to reach half the maximum angular displacement in a PENDULUM. Given that the bob hanging at rest was given an initial velocity of 2ms, and the length of the string is 6m.



2. Homework Equations
finding the angular velocity using sqrt.(g/l). where g is 9.8 and l is 6m.
maximum angular displacement with conservation of energy formulas.



3. The Attempt at a Solution

i found the maximum angular displacement and it is 68.8degrees using kinetic=potential energy. The question is half the maximum displacement so i took 34.4 degrees in radians, then i divided it by the angular velocity resulting in a wrong answer

The answer behind the book says 4.1s


Thanks any help is appreciated.
 
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The velocity is not constant.
What else could you do with the angle you found?
 
The speed is not uniform. To solve for the time, write the angular displacement as a function of time. (Hint: There'll be a trig function involved.)
 
got it, thanks a lot guys
 
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