# Simple Harmonic Motion with Linear Momentum

• lc99
In summary, the conversation discusses the conservation of momentum and energy in a scenario where a block is split into two halves. The equations T = 2pi * sqrt(m/k) and mv = m2v2 (LM) are used to calculate the velocity and amplitude of the two halves after separation. The conversation also raises the question of whether linear momentum is conserved in this scenario.
lc99

## Homework Equations

T = 2pi * sqrt(m/k)
mv =m2v2 (LM)[/B]

## The Attempt at a Solution

[/B]
So T2 depends on the mass and not velocity. So i can find T2 = 2pi * sqrt([m/2]/k)

For A2 , i know that the amplitude before any collision is 1/2m1v1^2 = 1/2kA1^2
so solving that, i get v1 = A1 sqrt(k/m) .

I know that linear moment is conserved so i can find v2...
m1v1=m2v2 --> mv1 = m/2 * v2 --> v2 = 2v1 = 2A1sqrt(k/m)

With the new velocity, v2, i writing with energy conservation...

1/2mv2^2 = 1/2kA2^2, so i can find A2 in terms of v2... and substituting v2 in terms of A1 from above
solving for A2, i would get A2 = mv2^2 / k = A2^2 --> A2 = sqrt(2A1)

did i do this correctly?

#### Attachments

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lc99 said:
I know that linear moment is conserved
That would mean transfer of momentum from the half mass removed to the half mass continuing. I don't read that in the scenario...

BvU said:
That would mean transfer of momentum from the half mass removed to the half mass continuing. I don't read that in the scenario...
so linear momentum isn't conserved?

Half the block is taken away, momentum included.

BvU said:
Half the block is taken away, momentum included.
I'm not sure what should be changed? How would i change my momentum equation?

lc99 said:
I'm not sure what should be changed? How would i change my momentum equation?
Consider the two halves of the block before and after separation. Before, each has momentum. If the separation does not involve any forces on them, what happens to each of the two momenta?

## 1. What is Simple Harmonic Motion with Linear Momentum?

Simple Harmonic Motion with Linear Momentum is a type of motion where an object moves back and forth in a straight line with a constant velocity. This motion is characterized by its periodicity, meaning the object repeats the same motion over and over again.

## 2. What are the factors that affect Simple Harmonic Motion with Linear Momentum?

The main factors that affect Simple Harmonic Motion with Linear Momentum are the mass of the object, the amplitude of the motion, and the frequency of the motion. The mass of the object affects the velocity of the motion, while the amplitude and frequency affect the distance and speed of the motion.

## 3. How is Simple Harmonic Motion with Linear Momentum different from other types of motion?

Simple Harmonic Motion with Linear Momentum is different from other types of motion because it involves the transfer of linear momentum between the object and the medium it is moving in. This is in contrast to other types of motion where the momentum is either conserved or transferred to other objects.

## 4. What is the equation for Simple Harmonic Motion with Linear Momentum?

The equation for Simple Harmonic Motion with Linear Momentum is x = A cos (ωt + φ), where x represents the displacement of the object, A is the amplitude of the motion, ω is the angular frequency, and φ is the phase constant.

## 5. What are some real-world examples of Simple Harmonic Motion with Linear Momentum?

Some examples of Simple Harmonic Motion with Linear Momentum in everyday life include the motion of a pendulum, the vibrations of a guitar string, and the motion of a mass attached to a spring. These motions can also be observed in the movement of waves, such as in water or sound waves.

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