Calculating the Frequency of Oscillation for an Oscillating Gate with Spring

AI Thread Summary
To calculate the frequency of oscillation for the gate, start with the equation for angular motion, which relates torque and angular displacement. The equation can be expressed as I * α = -k * θ, where I is the moment of inertia, α is the angular acceleration, k is the torsional spring constant, and θ is the angular displacement. The natural frequency of oscillation can be found using the formula ω = √(k/I). Given the values provided, substitute the moment of inertia and spring stiffness into the equation to find the frequency in radians per second. This approach will guide the calculation of the gate's oscillation frequency.
AdMitch
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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.
 
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it is very similar to F=ma for normal springs and masses

I\ddot\theta = ??

Can you complete the equation? (I is inertia)
 

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