- #1
Freya
- 15
- 1
Homework Statement
A system has 3 identical masses each connected by springs with stiffness k, and also with the end masses attached to a wall by a spring. The system is oscillating vertically. Write down the equations of motion for each of the masses, with the displacements of each mass denoted ψa, ψb and ψc.
Consider the scenario where ψb=0 and also ψa=-ψc and find the angular frequency of the system.
Homework Equations
F=ma, F=-kx
The Attempt at a Solution
For the equations of motion I got;
for the first mass: m(d2ψa/dt2)=(-Fψa/a)+(f/a)(ψb-ψa)
2nd: m(d2ψb/dt2)=(-Fψb/a)+(f/a)(ψc-ψb)
3rd: m(d2ψc/dt2)=(-Fψc/a)+(f/a)(ψc-ψb)
I have denoted a, myself, as the distance between the masses. I have also denoted F as the force exerted along the spring when the masses are displaced from equilibrium. Then by using small angle formulae (assuming the vertical displacement causes an angle between the spring and the horizontal to be <<1)
For the second part of this, I literally just plugged in the fact that ψb=0 and ended up with
ω=√(2F/ma)
Thank you for any assistance.
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