Mass-spring oscillator problem

In summary, the problem involves two masses accelerating towards each other with varying speeds before reaching the natural length of an elastic string. As they continue to approach each other while compressing the string, their speeds slow down at a constant velocity once the distance between them reaches the natural length of the string. The acceleration is caused by a decreasing tension in the string.
  • #1
aiyiaiyiai
5
0
Homework Statement
Two particles of equal mass (m) on a smooth horizontal table are connected by the a thin elastic string of natural length (a) in which a tension mg would produce an extension (a). The particles are held at rest at a distance (3a) apart.
i. Describe their motions between the time they are released and when they collide.
ii. If the particles are released simultaneously, calculate the time elapsed before they
collide, given a = 0.20 m.
Relevant Equations
F=kx
T=2*pi*sqrt(m/k)
I understand the masses will accelerate toward each other with the same varying speed before they reach the natural length of the spring. Then they continue to approach each other while compress the spring, that'll slow their speeds down definitely. So my question is, how could we calculate how long they take for the slowing-down process?
 
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  • #2
What you wrote would be true for a spring, but you don’t have a spring in this problem. You have a string.
 
  • #3
aiyiaiyiai said:
I understand the masses will accelerate toward each other with the same varying speed before they reach the natural length of the spring elastic string. Then they continue to approach each other while compress the spring, that'll slow their speeds down definitely at constant velocity once the distance between them has reached the value of a (natural length of the elastic string).
For each particle, you have acceleration from repose along distance a, and then constant final velocity along distance 0.5a (point of impact).
Note that the acceleration is caused by a variable or decreasing tension of the string.
 
  • #4
Lnewqban said:
For each particle, you have acceleration from repose along distance a, and then constant final velocity along distance 0.5a (point of impact).
Note that the acceleration is caused by a variable or decreasing tension of the string.
OMG, I didn't realize it is a string! thx!
 
  • #5
yes my bad. I didn't realize it is a string. 😂
vela said:
What you wrote would be true for a spring, but you don’t have a spring in this problem. You have a string.
 

1. What is a mass-spring oscillator problem?

A mass-spring oscillator problem is a physics problem that involves a mass attached to a spring and set in motion. The goal is to determine the motion of the mass over time, taking into account factors such as the mass, spring constant, and initial conditions.

2. What is the equation of motion for a mass-spring oscillator?

The equation of motion for a mass-spring oscillator is given by F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the mass from its equilibrium position.

3. How do you solve a mass-spring oscillator problem?

To solve a mass-spring oscillator problem, you can use the equation of motion and apply Newton's second law of motion (F = ma) to determine the acceleration of the mass. From there, you can use calculus to find the position and velocity of the mass at any given time.

4. What is the natural frequency of a mass-spring oscillator?

The natural frequency of a mass-spring oscillator is the frequency at which the mass will oscillate without any external forces acting on it. It is determined by the mass and the spring constant, and can be calculated using the equation f0 = 1/2π√(k/m).

5. How does the amplitude of a mass-spring oscillator change over time?

The amplitude of a mass-spring oscillator will decrease over time due to energy dissipation, such as friction and air resistance. This is known as damping. The rate of decrease in amplitude is determined by the damping constant, which can be calculated using the equation β = c/2m, where c is the damping coefficient and m is the mass.

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