Two springs supporting a mass verticle

In summary, the question is about finding the angular frequency of oscillation for two springs in a vertical position supporting an object of mass m with spring constants k1 and k2. The solution involves setting up an equation for force and acceleration, and using the fact that the displacement is measured from the equilibrium position, which already includes the effect of gravity. Therefore, gravity is not neglected in the solution.
  • #1
PsychonautQQ
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Homework Statement


Two springs have spring constants k1 and k2, are in a vertical position to support a single object of mass m. Show that the angular frequency of oscillation is ((k1+k2)/m)^(1/2) if the springs are in parallel.



The Attempt at a Solution




The book then goes on to explain
F = ma = -k1*x - k2*x
a + ((k1+k2)*x) / m = 0
where (k1+k2)/m = w^2
my question is why is gravity neglected?
 
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  • #2
They aren't really neglecting gravity. Note that the displacement (the x) is measured from the equilibrium position, so the effect of gravity is already included. (Gravity, being a constant force, merely shifts the zero point.)
 

1. How do the two springs affect the vertical motion of the mass?

The two springs work together to support the weight of the mass and provide a restoring force when the mass is displaced from its equilibrium position. This allows the mass to oscillate up and down in a harmonic motion.

2. How does the stiffness of the springs affect the system?

The stiffness, or spring constant, of the springs determines how much force is required to stretch or compress them. A higher spring constant means the springs are stiffer and will provide a stronger restoring force, resulting in a faster oscillation of the mass.

3. What is the equilibrium position of the mass in this system?

The equilibrium position is the point where the weight of the mass is balanced by the restoring force of the springs. In this system, the mass will be at rest when it is hanging at the midpoint between the two springs.

4. How does the mass affect the natural frequency of the system?

The mass affects the natural frequency of the system by changing the overall inertia and the amount of force required to move it. A heavier mass will result in a lower natural frequency, meaning the oscillations will be slower.

5. Can the two springs be replaced with a single spring?

Yes, the two springs can be replaced with a single spring, as long as the spring constant is equivalent to the combined spring constants of the two original springs. This single spring will act as a virtual spring, with the same effect on the system as the two separate springs.

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