Engineering Solving for Angular Velocity at Point A - Confused!

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The discussion revolves around confusion regarding the calculation of velocity at point A in relation to angular velocity. The user correctly determined the angular velocity but misapplied the cosine function, using cos45 instead of cos30 as required by the problem's parameters. There is a request for clearer presentation of the calculations, specifically asking for the use of LaTeX to improve readability. Participants emphasize the importance of accurately following the problem's specifications to arrive at the correct answer. Clear communication of mathematical work is essential for effective problem-solving in this context.
Pipsqueakalchemist
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Homework Statement
Questions and attempt below
Relevant Equations
Work energy theorem
So for this question I got the right angular velocity. But I don’t get the same velocity for point A. I don’t understand why it’s cos30, problem asked for V_a when theta = 45 so I used cos45. I have my work below.
 

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Your images of your work are pretty much illegible. Can you please type your work into the forum using LaTeX? See the LaTeX Guide link at the lower left. Thank you.
 
Thread 'Why wasn’t gravity included in the potential energy for this problem?'

Thread 'Why wasn’t gravity included in the potential energy for this problem?'

I’m looking at the attached vibration problem. The solution in the manual includes the spring potential energy but does NOT include the gravitational potential energy of the hanging mass. Can someone explain why gravitational potential energy is not included when deriving the equation of motion? I tried asking ChatGPT but kept going in circles and couldn't figure out. Thanks!
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