Vibration Problem: Determine Period

[RoyalFlush100]

Homework Statement

The uniform rod shown has mass 6 kg and is attached to a spring of constant k = 820 N/m. End B of the rod is depressed 10 mm and released.

Determine the period of vibration.

Picture is attached below

Homework Equations

Fs = kx
W = mg

The Attempt at a Solution

I honestly don't quite know how to even start a problem like this.
Fs = (820 N/m)(0.010 m) = 8.2 N
W = (6 kg)(9.81 N/kg) = 58.86 N
The spring force will act on the right end of the bar and the weight will act in the middle (@400 mm).

How am I supposed to proceed on this type of question? Do I need the torque about C?

 

[BvU]

You may assume the situation shown is the equilibrium position.
Clearly there is a restoring force trying to go back to equilibrium and there is some inertia in going there.
The restraint at point C makes that indeed you need to consider torque and moment of inertia, so you are on the right track. Proceed !

 

[Dr.D]

The easiest approach is to use energy methods, based on kinetic and potential energies.

 

[RoyalFlush100]

The easiest approach is to use energy methods, based on kinetic and potential energies.

How would that be done?
Initially the energy in the system would be the spring energy and perhaps relative gravitational energy. However, how would that be related to period?

 

[Dr.D]

Use conservation of energy to determine the equation of motion. The natural frequency falls out of the equation of motion, and the period is calculated from the natural frequency.