Effect of Breaking Mass on SHM Time Period & Amplitude

In summary, the question was about the effect on the time period and amplitude of oscillations if a mass attached to a ruler, lying horizontally on a table, is broken. The answer is that the amplitude would increase due to the inverse relationship between mass and amplitude, and the time period would decrease as it is directly proportional to mass. The formulas used to reach this conclusion were F = mr(omega)^2 and T^2 = 4 x pi^2 x m/k. The potential energy argument was also mentioned as a possible solution.
  • #1
chocofingers
30
0
Could anybody temme what wuld happen to the time period and the amplitude of oscillations if a mass attaching to a ruler, lying horizontally on the table, is broken ...then what effect would this have on the amplitude and time period of oscillations?

I say that amplitude would increase because mass is inversely proportional to amplitude and time period would decrease since it is directly proportional to mass...
the two formulas i derived my answers are...

F = mr (omega)^2

and T^2 = 4 x pi^2 x m/k

Am I right?
 
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  • #2
If I have understood your question (my english is not so good).
Using energy arguments if the mass brakes in two halfs when the potential energy is max, the potential energy is the same for the half attached to the spring since it just depends on the position of the mass, so the amplitude would be the same.
 
Last edited:
  • #3
u didnt get my question :(

np ... i solved it! :)
 

1. How does increasing the mass affect the time period of a simple harmonic motion (SHM) system?

Increasing the mass in a SHM system will result in an increase in the time period. This is because the mass is directly proportional to the inertia of the system, and greater inertia requires more time to complete one cycle of motion.

2. Does the amplitude of a SHM system change with the breaking mass?

Yes, the amplitude of a SHM system is affected by the breaking mass. Increasing the mass will result in a decrease in amplitude, while decreasing the mass will result in an increase in amplitude. This is because the mass affects the energy of the system, and a larger mass will require more energy to move, resulting in a smaller amplitude.

3. Is there a limit to how much the mass can be increased before the SHM system stops oscillating?

Yes, there is a limit to how much the mass can be increased before the SHM system stops oscillating. This limit is determined by the natural frequency of the system, and once the mass exceeds this limit, the system will no longer be able to complete a full cycle of motion.

4. How does the breaking mass affect the stability of the SHM system?

The breaking mass does not directly affect the stability of the SHM system. However, if the mass is increased beyond the limit mentioned in the previous question, the system may become unstable and stop oscillating.

5. Can the breaking mass change the frequency of a SHM system?

Yes, changing the breaking mass can affect the frequency of a SHM system. As the mass increases, the frequency decreases, and as the mass decreases, the frequency increases. This is because the frequency is inversely proportional to the square root of the mass, according to the equation T=2π√(m/k) where T is the time period, m is the mass, and k is the spring constant.

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