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In previous article we had an introduction with the system with the single degree of freedom, in this article we are going to study behavior of the system with the 1 degree of freedom which is undamped and is free to vibrate, without any external exciting force.
For undamped free vibrations, the damping force and the exciting force are equal to zero. Therefore the equation of motion of the system becomes
m.z'' + K.z = 0
or z'' + (K/m).z = 0 ---------eqn.(1)
The solution of the equation can be obtained by substituting
z= A1. cos.Wn.t + A2. sin.Wn.t
Where A1 and A2 are both constants and Wn is the undamped natural frequency.
when we substitute this value into the above eqn. (1), we get
Wn = (K/m)^(1/2)
It can be shown the final equation for the displacement will be again a sinusoidal wave with a phase angle at the start of the curve, i.e. at t=0.
In previous article we had an introduction with the system with the single degree of freedom, in this article we are going to study behavior of the system with the 1 degree of freedom which is undamped and is free to vibrate, without any external exciting force.
For undamped free vibrations, the damping force and the exciting force are equal to zero. Therefore the equation of motion of the system becomes
m.z'' + K.z = 0
or z'' + (K/m).z = 0 ---------eqn.(1)
The solution of the equation can be obtained by substituting
z= A1. cos.Wn.t + A2. sin.Wn.t
Where A1 and A2 are both constants and Wn is the undamped natural frequency.
when we substitute this value into the above eqn. (1), we get
Wn = (K/m)^(1/2)
It can be shown the final equation for the displacement will be again a sinusoidal wave with a phase angle at the start of the curve, i.e. at t=0.
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