# Solid pivoted pendulum attached to a spring – oscillation period?

**1. The problem statement, all variables and given/known data**

The figure shows a 200 g uniform rod pivoted at one end. The other end is attached to a horizontal spring. The spring is neither stretched nor compressed when the rod hangs straight down. What is the rods oscillation period? You can assume that the rods angle from vertical is always small.

**2. Relevant equations**

τ=2∏/ω

ω=√(k/M) for spring

ω=√(Mgl/I) for solid pendulum

**3. The attempt at a solution**

If not for the spring, this problem would simply be a solid pendulum, and the solution would simply be:

τ = [itex]\frac{2∏}{√(Mgl/I)}[/itex]

And if this were just a particle mass attached to the spring, the solution would be:

τ = [itex]\frac{2∏}{√(k/M)}[/itex]

I’m having trouble figuring out what happens to the equation in this case, though. One guess is as follows:

τ = [itex]\frac{2∏}{√(k/M) + √(Mgl/I)}[/itex]

But I’m clueless as to whether this is right or how to derive a correct equation. It seems like I might have to figure out the restoring force and/or torque in this case, but isn’t that just -kx and -MglΘ? If anyone could help me toward the right direction, I’d appreciate it.

http://ift.tt/1imriMj

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