Calculating Mass & Spring Constant for Oscillation

In summary, the conversation discusses a problem involving a block attached to a spring, with two different periods of oscillation when different masses are added. The equations T = 2pi*sqrt (m+2/k) and T = 2pi*sqrt ((m+2)/k) are used to solve for the mass of the block and the spring constant. The correct method involves solving both equations for k and setting them equal to each other to find the mass of the block.
  • #1
QuantumKnight
17
0

Homework Statement



A block with mass m is attached to the end of a spring with a constant spring k. It oscillates with a period of 2 seconds when pulled. When an additional 2 kg is add to the block it oscillates with a new period of 3 seconds. What is the mass of the black and the spring constant K?

Homework Equations


T = 2pi*sqrt (m+2/k) my apologies for the format. The symbols will not post for some reason.

The Attempt at a Solution


I attempted to use the about equation above and solve for m. Of course I ran into the problem that I do not know the spring constant k as well. I tried to find K by use the equation and solving for k by imputting the mass of the second block. However I am not confident because the period T at 3 seconds is when the masses are added together and not just for the 2 kg mass alone.

I am fine with the algrebra if I can just start the equation. Any help would be greatly appreciated.
 
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  • #2
You have two values for T, so that's two equations. For two unknowns. A little algebra and both come out just fine !
 
  • #3
Thank you for the response. Does this mean I solve both Period equations for k first then solve for mass?
 
  • #4
When solving for k: k =(8pi2)/4 = 2pi2
When solving for m: m = ((kT2)/(4pi2)) - 2
 
  • #5
QuantumKnight said:
When solving for k: k =(8pi2)/4 = 2pi2
When solving for m: m = ((kT2)/(4pi2)) - 2
That is not the right way to do this.

You have
T1 = 2pi*sqrt (m/k)
T2= 2pi*sqrt ((m+2)/k)
Now solve both equations for k because k is a constant and don't substitute anything in yet. Then you can set k's equal to each other and solve for m. After knowing the mass of the block you can calculate the spring constant k.
 
Last edited:
  • #6
Awesome, thank you
 

1. How do I calculate the mass and spring constant for oscillation?

To calculate the mass and spring constant for oscillation, you will need to know the period of oscillation and the amplitude of the oscillation. The mass can be calculated using the formula m = (4π²k)/T², where m is the mass, k is the spring constant, and T is the period. The spring constant can then be calculated using the formula k = (4π²m)/x², where x is the amplitude.

2. What is the relationship between mass and spring constant in oscillation?

The mass and spring constant have an inverse relationship in oscillation. This means that as the mass increases, the spring constant decreases, and vice versa. This relationship is described by the equation k = (4π²m)/x², where k is the spring constant, m is the mass, and x is the amplitude.

3. How does changing the mass affect the period of oscillation?

Changing the mass will directly affect the period of oscillation. As the mass increases, the period will also increase. This is because a higher mass will require more force to oscillate, resulting in a longer period. This relationship is described by the equation T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant.

4. Can the spring constant change in an oscillating system?

Yes, the spring constant can change in an oscillating system. This can happen if the spring itself is changed or if the oscillation is affected by external factors such as temperature or friction. It is important to note that the spring constant must remain constant for accurate calculations of mass and period.

5. How can I verify the accuracy of my calculated mass and spring constant?

The best way to verify the accuracy of your calculations is by performing multiple trials and comparing your results. Make sure to use the correct units and double-check your calculations to ensure accuracy. Additionally, you can compare your results to known values or consult with a peer or instructor for confirmation.

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