- #1

Xiothus

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- Homework Statement
- Hey guys, I'm a first year university student and I'm having trouble with this practice problem. I don't even really know where to start and thought this would be a good place to post for some help. The question is relating to harmonic motion and work + energy and goes as follows:

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Question:

A cylinder of mass M and radius R has an axle through its center. The

cylinder rolls without slipping back and forth along the x-axis. It has a

moment of inertia of (1/2)(M)(R^2). The axle is attached to a spring of spring constant k.

The origin is the place at which the mass experiences no force.

The cylinder is observed to undergo harmonic motion in the form x =A cos (ωt + φ).

What value of ω is consistent with the total energy being

constant?

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- Relevant Equations
- Circular motion equations + work and energy equations + angular momentum equations: up to first year university.

x = A cos (ωt + φ)

v = -Aωsin (ωt + φ)

a = -A(ω^2)cos (ωt + φ)

Thank you guys for taking the time to read this - I'm decently struggling with first year and need some tips on how to properly conceptualize problems and learn what the right approach is on certain problems.

Have a wonderful day, again thank you for checking this post out!

Have a wonderful day, again thank you for checking this post out!