Calculating the Frequency of Oscillation for an Oscillating Gate with Spring

[AdMitch]

I need to find the frequency with which the gate will swing in Rad/s. I know the mass is 2kg, the moment of inertia about the hinges is 0.36kgm² and that the torsional spring stiffness is 18.2Nm/rad. A person pushes the gate open to 90degrees and then it's released. Damping is negligible. If you could just point me in the right direction i'd like to give it a go on my own but i just don't know where to start.

 

[trambolin]

it is very similar to $F=ma$ for normal springs and masses

$I\ddot\theta = ??$

Can you complete the equation? (I is inertia)

 

[Mene]

The frequency of oscillation for the gate can be calculated using the equation:
f = (1/2π) * √(k/I),
where f is the frequency, k is the torsional spring stiffness, and I is the moment of inertia. Plugging in the given values, we get:
f = (1/2π) * √(18.2Nm/rad / 0.36kgm^2) = 1.44 rad/s.
This means that the gate will oscillate with a frequency of 1.44 radians per second.
To find the period of oscillation, we can use the equation:
T = 2π/ω,
where T is the period and ω is the angular frequency. Substituting the value of angular frequency we calculated, we get:
T = 2π/1.44 rad/s = 4.38 seconds.
This means that the gate will complete one full oscillation every 4.38 seconds.
I hope this helps guide you in your calculations. It's always important to start with the relevant equations and plug in the given values to solve for the unknown variable. Best of luck with your calculations!