Period of oscillation of spring system

In summary, the conversation is about a system consisting of two blocks connected by a spring and shoved against a wall. The question is to determine the period of oscillation when the left block is no longer in contact with the wall. The solution involves finding the reduced mass (M/2) and using the equation for the period of oscillation (2(pi)sqrt(m/k)). The explanation given is to divide the spring into two halves and consider each half to be fixed against a wall, thus doubling the spring constant and keeping the mass as M. The conversation also includes a request for a qualitative description of the motion and a link to an animation to better understand the problem.
  • #1
SbCl3
6
0
1. Question
A system consists of two blocks, each of mass M, connected by a spring of force constant k. The system is initially shoved against a wall so that the spring is compressed a distance D from its original uncompressed length. The floor is frictionless. The system is now released with no initial velocity. (See picture)

[part c] Determine the period of oscillation for the system when the left-hand block is no longer in contact with the wall.

Homework Equations



period = 2(pi)sqrt(m/k)

The Attempt at a Solution



The answer given is this: period = 2(pi)sqrt(M/(2k))
The explanation given is "m = reduced mass = M/2".

I don't understand the explanation given. I can't visualize what happens to the right mass M after the left mass M leaves the wall. This is different from all spring problems I have seen, where one end is attached to a wall, so of course I suspect a different answer. Could someone show me the math involved to prove the period is reduced like this?
 

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  • #2
SbCl3 said:
The answer given is this: period = 2(pi)sqrt(M/(2k))
The explanation given is "m = reduced mass = M/2".

I don't understand the explanation given. I can't visualize what happens to the right mass M after the left mass M leaves the wall. This is different from all spring problems I have seen, where one end is attached to a wall, so of course I suspect a different answer. Could someone show me the math involved to prove the period is reduced like this?

Hi SbCl3! :smile:

Divide the spring into two halves, then you can consider each half to be fixed against a wall (in c.o.m. frame of reference, of course) … the spring constant is doubled (1/K = 1/k + 1/k), and the mass is M :wink:
 
  • #3
Can anyone please describe the motion qualitatively? I cannot visualize this problem. After the blow, the spring is maximally compressed and the block on the right moves to the right, away from the wall. I know that the left mass leaves the wall the first time that the right mass has its maximum speed to the right and the spring is at its equilibrium length. But I have no idea how the motion is after that.

All help appreciated.
Thanks
 
  • #4
Please help this question has been giving me nightmares.
 
  • #5
does anyone have a link to an animation
 
  • #6
guys?
 

1. What is the period of oscillation of a spring system?

The period of oscillation of a spring system is the amount of time it takes for the spring to complete one full cycle of motion. It is typically measured in seconds.

2. How is the period of oscillation calculated for a spring system?

The period of oscillation for a spring system can be calculated using the formula T=2π√(m/k), where T is the period, m is the mass attached to the spring, and k is the spring constant.

3. Does the mass attached to the spring affect the period of oscillation?

Yes, the period of oscillation is directly proportional to the mass attached to the spring. A heavier mass will result in a longer period of oscillation, while a lighter mass will result in a shorter period of oscillation.

4. How does the spring constant affect the period of oscillation?

The spring constant also has a direct effect on the period of oscillation. A higher spring constant will result in a shorter period of oscillation, while a lower spring constant will result in a longer period of oscillation.

5. Are there any other factors that can affect the period of oscillation for a spring system?

Yes, external factors such as damping, friction, and air resistance can also affect the period of oscillation for a spring system. These factors can cause the spring to lose energy and slow down, resulting in a longer period of oscillation.

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