Amplitude of SHM of a spring hung from a ceiling

In summary, the conversation revolved around a poorly worded question about a point mass suspended by a massless string and its equation of simple harmonic motion. The confusion stemmed from unclear information and an incorrect answer key, leading to discussion about the mean position, amplitude, and phase.
  • #1
Vriska
138
2

Homework Statement


A point mass of m = 20 kg is suspended by a massless of constant 2000N/m. The point mass is released when the elongation is 15cm.Find equation of shm

Homework Equations



F= - kx

The Attempt at a Solution

[/B]

I'm not sure what this question is trying to say honestly. But - I'd say the mean position would be at x = 10 cm and since they release it at 15 cm, I'd expect the amplitude to be 5 cm.

But they've said the amplitude is A = mg/x in the answer , which I don't quite process. And they've done something and found the phase to be off by pi/6. Is this just a badly worded question or am I wooshing somewhere?
 
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  • #2
Vriska said:
Is this just a badly worded question
I'd say it's a badly worded question (or an error in the answer key). Is it from a textbook?
 
  • #3
Doc Al said:
I'd say it's a badly worded question (or an error in the answer key). Is it from a textbook?

It's from a workbook for an exam :/ thanks for confirming my suspicions though, I've already seen quite a few badly worded problems here and suspected this might also be one
 
  • #4
Vriska said:
But they've said the amplitude is A = mg/x in the answer
That expression doesn't even have the correct dimensions for an amplitude. (Unless that x was meant to be a 'k'.)
 

FAQ: Amplitude of SHM of a spring hung from a ceiling

What is the amplitude of SHM of a spring hung from a ceiling?

The amplitude of SHM (Simple Harmonic Motion) of a spring hung from a ceiling is the maximum displacement from equilibrium position. It is the distance between the equilibrium position and the farthest point that the spring can stretch or compress.

How is the amplitude of SHM affected by the properties of the spring?

The amplitude of SHM is directly proportional to the properties of the spring, such as its stiffness or spring constant, and its mass. A stiffer spring or a heavier mass will result in a larger amplitude, while a less stiff spring or a lighter mass will result in a smaller amplitude.

What factors can affect the amplitude of SHM of a spring?

The amplitude of SHM can be affected by the initial displacement of the spring, the properties of the spring, such as its stiffness and mass, and the presence of any external forces or damping. Additionally, the amplitude may also change over time as the spring loses its energy due to friction or other dissipative forces.

How can the amplitude of SHM be calculated?

The amplitude of SHM can be calculated using the equation A = xmax - xeq, where A is the amplitude, xmax is the maximum displacement from equilibrium position, and xeq is the equilibrium position. Alternatively, the amplitude can also be determined by measuring the distance between the extreme positions of the spring during one complete cycle of oscillation.

What is the significance of the amplitude of SHM in a spring hung from a ceiling?

The amplitude of SHM is an important characteristic of a spring's motion as it determines the range of motion of the spring and the maximum potential energy it can store. It also affects the frequency and period of the oscillations, and thus is crucial in understanding the behavior of a spring in SHM.

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