A mass between two springs-simple harmonic motion

In summary: and total p.e= 1/2kx^2 +1/2kx^2 = 1/2*(40)*16=320 joule (since both the spring has same displacement 4m).
  • #1
cnputhur
1
0

Homework Statement


A 4kg mass remains at rest on a friction free surface due to equal and opposite pulls of two springs. Spring 1 is stretched 4 meters. The k in spring 1 equals 40 N/m and the k in spring 2 equals 60 N/m.

This is what the the picture looks like in words.
From left to the right, these are the objects.

Wall, spring 1, 4kg mass, spring 2, wall

1. How much is spring 2 stretched?
2. What is the potential energy stored in each spring?
3. Taken as a simple harmonic motion system, what is the potential energy stored in the system

Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


F=ma
Restorative force=-kx perhaps?

The Attempt at a Solution


1. F=-kx=-40(4)=-160N
160=-kx=-60x
x=-8/3 meters
8/3 meters to the left?

2. PE=0.5kx^2=0.5(40)(4)^2=320J in Spring 1
PE=0.4kx^2=0.5(60)(-8/3)^2=640/3 J in Spring 2

3. 320+(640/3)=1660/3 J

I'm very unsure about these answers. To be honest, I don't understand the questions.
 
Last edited:
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  • #2
Hello cnputhur, welcome to PF.

Your solution to the first question is the correct magnitude. However your minus signs may have gone awry. Try labeling the forces in future to help with these things ( a diagram will then make it very clear which way it must go).

And for question 2?...
 
  • #3
cnputhur said:

Homework Statement


A 4kg mass remains at rest on a friction free surface due to equal and opposite pulls of two springs. Spring 1 is stretched 4 meters. The k in spring 1 equals 40 N/m and the k in spring 2 equals 60 N/m.

This is what the the picture looks like in words.
From left to the right, these are the objects.

Wall, spring 1, 4kg mass, spring 2, wall

1. How much is spring 2 stretched?
2. What is the potential energy stored in each spring?
3. Taken as a simple harmonic motion system, what is the potential energy stored in the system?



Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations


F=ma
Restorative force=-kx perhaps?



The Attempt at a Solution


F=-kx=-40(4)=-160N
160=-kx=-60x
x=-8/3 meters
8/3 meters to the left?

f=kx. -ve sign only indicates it is in the opp. direction.
about energy, spring p.e. =1/2kx^2
 

Related to A mass between two springs-simple harmonic motion

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object moves back and forth between two points, with its acceleration and displacement being directly proportional to each other. This type of motion is commonly observed in systems that involve a mass attached to a spring.

2. How does a mass between two springs exhibit simple harmonic motion?

A mass between two springs exhibits simple harmonic motion when it is displaced from its equilibrium position and then released. The two springs on either side of the mass act as restoring forces, causing the mass to oscillate back and forth between them.

3. What is the relationship between the mass, spring constant, and period in a simple harmonic motion system?

In a simple harmonic motion system, the period (T) is directly proportional to the square root of the mass (m) and inversely proportional to the square root of the spring constant (k). This means that as the mass increases, the period also increases, but as the spring constant increases, the period decreases.

4. Can the amplitude of a mass between two springs change?

Yes, the amplitude of a mass between two springs can change if an external force is applied to the system. However, in an ideal system with no external forces, the amplitude remains constant and the motion is considered "simple" harmonic.

5. Are there any real-life examples of simple harmonic motion involving a mass between two springs?

Yes, there are many real-life examples of simple harmonic motion involving a mass between two springs. Some common examples include pendulum clocks, car suspension systems, and tuning forks. These systems all involve a mass attached to a spring or elastic material that undergoes back-and-forth motion.

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