Calculate Time for Mass to Reach Equilibrium Position

In summary, the conversation discusses the time required for a load of mass .2 g, hanging from a light spring with an elastic constant of 20 N/m, to reach its equilibrium position after being pulled down .1 m and released. The correct time is found to be T/4, which is equal to .157 s based on the formula T=2pi(square root(m/k))=.628s.
  • #1
timtng
25
0
A load of mass .2 g is hanging from a light spring whose elastic constant is 20 N/m. The load is pulled down .1 m from its equilibrium position and released.

How long is required for the load to reach its equilibrium position?

T=2pi(square root(m/k))=.628s

Please verify to see if I did it correctly.

Thanks
 
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  • #2
I'm not looking carefully, but you seem to be wrong. It asks the time taken to reach the initial equilibrium position, while you seem to have given the periodic time for an oscillation in SHM, which would be 4*t.
 
  • #3
so the answer should be T/4?
 
  • #4
Yes. The "T" you give is the time to go up to the maximum height, then back down to the initial position: 1 cycle. The weight will take exactly 1/4 of that time to go back to the equilibrium point (1/2 T to reach the highest point, 3/4 T to pass the equilibrim point again and then at T back to the initial point).
 
  • #5
so t should equal to .628s/4 = .157 s
 

FAQ: Calculate Time for Mass to Reach Equilibrium Position

How do you calculate the time for mass to reach equilibrium position?

To calculate the time for mass to reach equilibrium position, you will need to know the mass of the object, the spring constant, and the displacement from the equilibrium position. Then, you can use the formula T = 2π√(m/k) where T is the time, m is the mass, and k is the spring constant.

What is the significance of the equilibrium position in this calculation?

The equilibrium position is the point at which the forces acting on the object are balanced. It is important to know this position because it is the starting point for calculating the displacement and determining the time it takes for the mass to reach this point.

Can the time for mass to reach equilibrium position be calculated for any type of object?

The formula for calculating the time for mass to reach equilibrium position is specifically for objects attached to a spring. However, similar principles can be applied to other systems, such as a pendulum or a simple harmonic oscillator, to calculate the time it takes for the object to reach its equilibrium position.

Is the time for mass to reach equilibrium position affected by the amplitude of the oscillation?

Yes, the amplitude of the oscillation will affect the time it takes for the mass to reach equilibrium position. The larger the amplitude, the longer it will take for the object to reach the equilibrium position. This is because a larger amplitude means a larger displacement, which will require more time for the object to cover.

Can the time for mass to reach equilibrium position be measured experimentally?

Yes, the time for mass to reach equilibrium position can be measured experimentally by setting up a simple pendulum or a spring system and measuring the time it takes for the object to complete one full oscillation. This can be repeated for different masses and spring constants to verify the calculated time using the formula.

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