Displacement of a spring

In summary, the problem involves a 0.24 kg mass suspended on a spring, which is stretched 5.9 cm before being pulled down an additional 13.5 cm and released. The question asks for the displacement from the equilibrium position after 0.46 s. The equation to solve for this involves finding the spring constant, using the cosine equation with a negative amplitude, and taking into account the initial spring stretch and the extra distance pulled.
  • #1
thesandalman
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0

Homework Statement



A 0.24 kg mass is suspended on a spring which stretches a distance of 5.9 cm. The mass is then pulled down an additional distance of 13.5 cm and released. What is the displacement from the equilibrium position with the mass attached (in cm) after 0.46 s? Take up to be positive and use g = 9.81 m/s2.

Homework Equations



Hint:
Get k from the displacement as it was done in this example. The equation will have
ω = (k/m)1/2,

and the phase will be such that it will be a cosine with a negative amplitude, because it starts at a negative displacement.

Be careful about the sign!
You have to get
y=-x[0]*cos(sqrt(t^2*g/x))
where from the eq-position
it follows that omega=sqrt(g/x)


The Attempt at a Solution



I tried doing the equations stated above however, I am still confused. I was not sure if x[0] means the distance the spring stretches at first or what? Also if X would then be the initial spring stretch + the extra distance pulled or what? Any help would be must appreciated!
 
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  • #2
x[0] is simply the amplitude, i.e. maximum displacement from the equilibrium position.

The equilibrium position is defined as the position of the mass when there is no oscillation, so go figure out if you need to add up 13.5 cm and 5.9 cm or not.

After that find the spring constant k and then just use that cosine equation to solve for the displacement.
 

1. What is displacement of a spring and how is it measured?

The displacement of a spring refers to the distance that the spring has been stretched or compressed from its original position. It is typically measured in meters (m) or centimeters (cm) using a ruler or other measuring instrument.

2. What factors affect the displacement of a spring?

The displacement of a spring is affected by its stiffness or spring constant, the amount of force applied to it, and the length of the spring. The type of material the spring is made of can also affect its displacement.

3. How does Hooke's Law relate to the displacement of a spring?

Hooke's Law states that the force exerted by a spring is directly proportional to its displacement. This means that the more the spring is stretched or compressed, the greater the force applied to it will be.

4. Can the displacement of a spring be negative?

Yes, the displacement of a spring can be negative if it is compressed instead of stretched. In this case, the displacement would be represented by a negative value, but it still follows the same principles of Hooke's Law.

5. How is the displacement of a spring used in real-life applications?

The displacement of a spring is used in various real-life applications such as in suspension systems for vehicles, in shock absorbers, and in mechanical watches. It is also used in scientific experiments to measure the elasticity of materials and to determine the force required to stretch or compress a spring by a certain amount.

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