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

Thread starter SafiBTA
Start date Today, 8:46 PM
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Kinetic energy Potential energy Spring mass system Vibrations

Today, 8:46 PM

SafiBTA

Homework Statement: Derive the equation of motion using the principle of conservation of energy

Relevant Equations: T = ½ m ẋ² + ½ J₀ θ̇²

x = 4 r θ

U_spring = ½ k (4 r θ)²

(What’s confusing me is: shouldn’t there also be a gravitational potential term U_g = m g x ?)

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!

Last edited: Today, 9:35 PM

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