# Harmonic Motion Help: Solving After Collision

• jaymay
In summary, the conversation discusses a problem involving a vibrating system of a particle attached to a spring. A 6.00-kg object is dropped on top of the 4.00-kg particle, causing a change in amplitude, period, and energy. The solution involves treating the collision as inelastic and using conservation of momentum and energy to find the new amplitude and energy. The vertical motion is not a factor in the problem.
jaymay
I am having trouble with this problem:

A particle of mass 4.00 kg is attached to a spring with a force constant of 100 N/m. It is oscillating on a horizontal frictionless surface with an amplitude of 2.00 m. A 6.00-kg object is dropped vertically on top of the 4.00-kg object as it passes through its equilibrium point. The two objects stick together.
(A) By how much does the amplitude of the vibrating system change as a result of the collision.
(B) By how much does the period change?
(C)By how much does the energy change?
(D) Account for the change in energy?

This is pretty much a plug-in problem, but my main question is how to solve for the new amplitude and energy after the collision. I am going over the formulas and it seems like the amplitude is in the formula for energy and energy is part of the formula for amplitude, how can I solve for one or the other when they both change after the collision? Can someone give me a clue?

jaymay said:
I am having trouble with this problem:

A particle of mass 4.00 kg is attached to a spring with a force constant of 100 N/m. It is oscillating on a horizontal frictionless surface with an amplitude of 2.00 m. A 6.00-kg object is dropped vertically on top of the 4.00-kg object as it passes through its equilibrium point. The two objects stick together.
(A) By how much does the amplitude of the vibrating system change as a result of the collision.
(B) By how much does the period change?
(C)By how much does the energy change?
(D) Account for the change in energy?

This is pretty much a plug-in problem, but my main question is how to solve for the new amplitude and energy after the collision. I am going over the formulas and it seems like the amplitude is in the formula for energy and energy is part of the formula for amplitude, how can I solve for one or the other when they both change after the collision? Can someone give me a clue?

Ignore the spring forces during collision and treat the collision in terms of conservation of momentum. The vertical component will not be a factor; the normal force will stop the vertical motion. Horizontal momentum will be conserved. Calculate the kinetic energy after the collision. Use that to find the maximum displacement of the spring. Use the new mass to find the new period/frequency.

I don't see a "collision". You are not told the height from which the new mass is dropped and it is, anyway, vertical, which will not affect horizontal motion.

The only thing that happens is that the mass suddenly changes from 4 to 10 kg.

HallsofIvy said:
I don't see a "collision". You are not told the height from which the new mass is dropped and it is, anyway, vertical, which will not affect horizontal motion.
While the vertical motion doesn't matter, the horizontal motion does. Treat this as an inelastic collision between the moving 4 kg particle and the stationary 6 kg object.

Thanks for all the help. I was able to solve the problem as you all suggested by treating it as an inelastic collision. I solve for the energy of the system before the collision. Using the result of the energy I was able to solve for the initial velocity. Once I had the initial velocity I was able to solve for the final velocity by treating it as an ineslatic collision. Once I had the final velocity, I was able to solve for the new Amplitude and the rest was just plug-in. Thanks again for all the help.

## 1. What is harmonic motion?

Harmonic motion is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point. It is characterized by a restoring force that is directly proportional to the displacement of the object from the equilibrium point.

## 2. What happens to the motion of an object after a collision?

After a collision, the motion of an object will depend on the type of collision that occurred. In an elastic collision, the objects will bounce off each other with no loss of kinetic energy. In an inelastic collision, the objects will stick together and move with a common velocity. In both cases, the total momentum of the objects will be conserved.

## 3. How do you solve for the motion of an object after a collision?

To solve for the motion of an object after a collision, you will need to use the principles of conservation of momentum and conservation of energy. You will also need to consider the type of collision and the properties of the objects involved, such as mass and velocity.

## 4. What is the difference between elastic and inelastic collisions?

In an elastic collision, the objects involved bounce off each other with no loss of kinetic energy. In an inelastic collision, the objects stick together and move with a common velocity, resulting in a loss of kinetic energy. In both cases, the total momentum of the objects is conserved.

## 5. How does the concept of harmonic motion apply to collisions?

The concept of harmonic motion applies to collisions in the sense that the objects involved will experience oscillatory motion around an equilibrium point. The restoring force in this case is provided by the collision itself, as the objects try to return to their original positions before the collision. This results in a periodic motion that can be described using harmonic motion equations.

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