Finding the time period of this System

In summary: If the mass feels a force of mg-kx/4 at the displaced position then the equation of motion will be:(m+kx)x+T=0 which gives us the equation of motion for the simple harmonic motion.In summary, the mass will experience a force of mg-kx/4 at the displaced position, which will give the equation of motion for the simple harmonic motion.
  • #1
Hydrous Caperilla
62
7

Homework Statement


To find the time period of this simple harmonic motion

Homework Equations


F= -kx

The Attempt at a Solution


To check Simple harmonic motion first ,I have to displace the mass by some distance which I take to be x in this case.

Therefore the spring will be displaced by a distance 2x and a spring force of 2kx will act on the pulley from the spring since it is massless and hence due to Third law of motion I think.I don't know how to proceed after this
 

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  • #2
Hydrous Caperilla said:
Therefore the spring will be displaced by a distance 2x
You need to rethink this.
 
  • #3
Orodruin said:
You need to rethink this.
I got struck after this...I need to know how the Third law will affect the pulley more after this but I can't get a clear idea of that
 
  • #4
Hydrous Caperilla said:
I got struck after this
You misunderstand me. Your statement was wrong, so you need to rethink it.

Apart from that, what do you get when you apply the third law to different subsystems, for example, the pulley, the mass, etc?
 
  • #5
I have no idea about that...
 
  • #6
I am sorry, but we can only show you the path. You need to walk it yourself.

What exactly is your difficulty in writing down the forces that act on, for example, the pulley?
 
  • #7
The pulley will feel spring force due to the elongation of spring but How would this force be countered...I f I get that then this will probably help me a lot
 
  • #8
You are missing some of the forces that act on the pulley. Note that we are only talking about the pulley now. Not the system as a whole, only the pulley subsystem.
 
  • #9
Orodruin said:
You are missing some of the forces that act on the pulley. Note that we are only talking about the pulley now. Not the system as a whole, only the pulley subsystem.

So will it balanced by Tension
 
  • #10
Yes, so how does Newton's third law look for the pulley?
 
  • #11
Both sides of pulley will experience a force of kx/4 to counter the force(I messed up the spring force on pulley)
 
  • #12
Both sides of pulley will experience a force of kx/4 to counter the force(I messed up the spring force on pulley)
 
  • #13
So what does this mean for the force balance of the mass?
 
  • #14
So now the mass will feel mg-kx/4 force at the displaced position
 
Last edited:
  • #15
Which means what for the equation of motion?
 

Related to Finding the time period of this System

1. How do you determine the time period of a system?

The time period of a system can be determined by observing the system's motion and measuring the time it takes for one complete cycle or revolution. This can be done using a stopwatch or by analyzing data from a motion sensor.

2. What factors affect the time period of a system?

The time period of a system can be affected by various factors such as mass, length, and stiffness. The more massive the system is, the longer it takes to complete one cycle. Similarly, a longer length or higher stiffness can also increase the time period.

3. Can the time period of a system change over time?

Yes, the time period of a system can change over time due to external factors such as friction, air resistance, or changes in the system's parameters. These changes can alter the system's dynamics and affect its time period.

4. How does a pendulum's length affect its time period?

The length of a pendulum directly affects its time period. The longer the pendulum, the longer it takes to complete one swing. This is because a longer pendulum has a larger arc length and takes more time to cover it.

5. Can the time period of a system be calculated using a mathematical formula?

Yes, the time period of a system can be calculated using various mathematical formulas, depending on the type of system. For example, the time period of a simple pendulum can be calculated using the formula T = 2π√(L/g), where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity.

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