How Is Spring Constant Calculated in Simple Harmonic Motion?

In summary, the conversation discusses a problem involving a fisherman's scale and a fish hanging from it. The question asks for the spring constant and the amplitude and frequency of vibration if the fish is pulled down and released. The conversation also mentions equations for potential energy and position, but the solution is found using Hooke's law. The amplitude is given in the question and the conversation concludes with encouragement to ask questions and clarification on the concept of amplitude.
  • #1
meganw
97
0

Homework Statement



A fisherman's scale stretches 3.4 cm when a 3.3 kg fish hangs from it.

(a) What is the spring constant?

(b) What will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down?

Homework Equations



I know that the PE of a spring is .5kA
I also know that x=Asinwt

But I don't know t, so I can't see how I'd use that equation either.

The Attempt at a Solution



I know that equation, but how can I set it equal to the KE of the spring when I don't know the velocity of the spring at all?? I thought this might be a conservation of energy problem but I don't see how that would work out.
 
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  • #2
Have you met Hooke's law yet?
 
  • #3
I got it right now, (thank you! =) But how do you find the amplitude on part b?? I don't know the PE, or time...

I'm sorry we just learned this and I'm really confused still.
 
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  • #4
meganw said:
I got it right now, (thank you! =) But how do you find the amplitude on part b?? I don't know the PE, or time...
But surely you can just see the amplitude, it's given to you in the question..:wink:
meganw said:
I'm sorry we just learned this and I'm really confused still.
Not a problem, and you don't have to apologise for asking questions, you should always ask questions :smile:
 
  • #5
The amplitude of a SHM system is how far the object has been stretched from it's initial position.
 

Related to How Is Spring Constant Calculated in Simple Harmonic Motion?

What is simple harmonic motion?

Simple harmonic motion is a type of periodic vibration or oscillation where the restoring force is directly proportional to the displacement from equilibrium. It is characterized by a sinusoidal pattern and is often seen in systems with a restoring force, such as a mass on a spring or a pendulum.

What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x(t) = A sin(ωt + φ), where x(t) is the displacement from equilibrium at time t, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

What is the difference between simple harmonic motion and uniform circular motion?

In simple harmonic motion, the restoring force is directly proportional to the displacement from equilibrium, while in uniform circular motion, the force is always directed towards the center of the circle. In simple harmonic motion, the motion is linear, while in uniform circular motion, the motion is circular.

What is the relationship between simple harmonic motion and energy?

In simple harmonic motion, the total energy of the system remains constant. The potential energy is at its maximum at the turning points, while the kinetic energy is at its maximum at the equilibrium point. This means that the energy is constantly being exchanged between potential and kinetic energy, but the total energy remains the same.

How is simple harmonic motion applied in real life?

Simple harmonic motion can be seen in many real-life systems, such as pendulums in clocks, springs in mattresses or car suspensions, and even in sound waves. It is also used in various engineering applications, such as designing shock absorbers or tuning musical instruments.

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