Mass attached to vertical spring

In summary, an object with a mass of 0.4kg is attached to a horizontal spring with a spring constant of 80N/m. It is displaced 0.1m from the equilibrium position and released from rest, performing simple harmonic motion. The velocity of the object when it passes through the equilibrium point can be found by solving the equation ke=0.5(mg)^2/k. The attempt at a solution yields v=0.7, but the solution key states it should be 1.4m/s (ref: Serway Physics vol 8, ch#13, pg451, question 4). To solve, a free body diagram for the mass should be sketched and NII should be written
  • #1
sualeh
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Homework Statement



an object of mass 0.4kg is attached to horizontal spring of ,,spring constant 80N/m,,and it is displaced 0.1m from equilibrium postion and released from rest,,such that it perform up and down simple harmonic motion.find its velocity when it passes through equilibrium point

Homework Equations



k.e=kinetic energy...k.e=0.5><(mg)^2/k...

3. The attemp at a solution
solving above equation will give,,v=0.7,,,but in solution key it is 1.4m/s ref(serway physics vol 8..ch#13,pg451,,ques,4
 
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  • #2
Sketch a free body diagram for the mass and write NII for its motion. Then use the initial conditions to find the position of the mass as a function of t, from which you can obtain its velocity as a function of t.
 

Related to Mass attached to vertical spring

1. What is the relationship between the mass attached to a vertical spring and its displacement?

The relationship between the mass attached to a vertical spring and its displacement is described by Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. This means that the greater the mass attached to the spring, the greater the force and displacement will be.

2. How does the stiffness of the spring affect the motion of the mass?

The stiffness of the spring, also known as the spring constant, determines how much force is required to stretch or compress the spring. A stiffer spring will result in a faster and more intense motion of the mass, while a less stiff spring will result in a slower and less intense motion.

3. Can the oscillation of the mass on the spring be affected by external factors?

Yes, the oscillation of the mass on the spring can be affected by external factors such as air resistance, friction, and damping. These factors can alter the oscillation frequency and amplitude of the mass-spring system.

4. How does the amplitude of the mass-spring system change with varying mass and spring stiffness?

The amplitude of the mass-spring system is directly proportional to the mass attached to the spring and the square root of the spring stiffness. This means that as the mass or stiffness increases, the amplitude will also increase.

5. What is the period of oscillation for a mass attached to a vertical spring?

The period of oscillation for a mass attached to a vertical spring can be calculated using the formula T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. This means that the period is influenced by the mass and stiffness of the spring, with a larger mass or stiffer spring resulting in a longer period of oscillation.

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