Vibrating Spring without Damping. A vibrating spring without damping can be modeled by the initial value problem in Example by taking .
a) If , and , find the equation of motion for this undamped vibrating spring.
b) After how many seconds will the mass in part first cross the equilibrium point?
c) When the equation of motion is of the form displayed in , the motion is said to be oscillatory with frequency . Find the frequency of oscillation for the spring system of part .
The differential equation without damping is
Then the auxiliary equation is
Therefore, the general solution is .
Given initial conditions are and
Therefore, the solution is .
When the spring crosses the equilibrium , so we have to find the
So, at seconds the mass crosses the equilibrium
Here , the Frequency of the spring is .
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