Mass m suspended by two springs in series

[idir93]

Hello guys I'm desperately trying to understand the solution of this assignement .
What would be the differential equation og this Simple Harmonic Motion when you have a mass m suspended to 2 springs in series ?

 

[Puneeth423]

Hello guys I'm desperately trying to understand the solution of this assignement .
What would be the differential equation og this Simple Harmonic Motion when you have a mass m suspended to 2 springs in series ?

[kx - mg = m (dv/dt) = m(d sqaure x/dt)]

 

[haruspex]

What would be the differential equation og this Simple Harmonic Motion when you have a mass m suspended to 2 springs in series ?

If the springs are considered massless, what do you think the relationship would be between the tensions in the two springs?

 

[idir93]

If the springs are considered massless, what do you think the relationship would be between the tensions in the two springs?

yes the springs are massless, i got this answer from a textbook : the tension is uniform in the upper spring and has a magnitude of kx, hence the tension in the lower spring also has a magnitude of kx
the displacement of M is 2x.
the diff eq is :
M2(dx²)/(dt) + kx = 0

Why 2 in the first argument and not in the second since we have two springs.

 

[Doc Al]

See if you can figure out what the effective spring constant is for the two springs in series.

 

[idir93]

See if you can figure out what the effective spring constant is for the two springs in series.

that's the problem my friend :( it's the reverse of series resistors on a circuit.
K (equivalent) = (k1k2)/(k1 + k2)
But i don't know how to get to it. maybe by moving backward

 

[Doc Al]

that's the problem my friend :( it's the reverse of series resistors on a circuit.
K (equivalent) = (k1k2)/(k1 + k2)
But i don't know how to get to it. maybe by moving backward

Compare the force stretching the springs to the overall amount of stretch. How does the overall system stretch compare to that of each spring?

 

[idir93]

How ?

 

[Doc Al]

How ?

Imagine two springs in series, with spring constants k₁ and k₂. A force F stretches the two springs, thus F = k₁x₁ = k₂x₂.

For the system as a whole, you have:
F = k'(x_total)

See if you can solve for k'.

 

[idir93]

how can i get rid of x1 and x2 ?

 

[Doc Al]

how can i get rid of x1 and x2 ?

Express them in terms of F and k.

 

[idir93]

Thanks i did it with your big help, but i still don't understand this case when k1=k2 and x1=x2 because in my problem the two springs have the same k and since they are massless they'll be stretchend with the same x making a total of 2x in the displacement.
Why in the first argument of the diff eq we have M2(dx²)/(dt) and in the 2nd we just have kx not 2kx ?

 

[idir93]

It's okay now i totally got it thank you very much for your help :) please tell me which degree do you have ?

 

[Doc Al]

Thanks i did it with your big help, but i still don't understand this case when k1=k2 and x1=x2 because in my problem the two springs have the same k and since they are massless they'll be stretchend with the same x making a total of 2x in the displacement.

When k1 = k2, k' = k/2.

Why in the first argument of the diff eq we have M2(dx²)/(dt) and in the 2nd we just have kx not 2kx ?

d²x/dt² + k'x = 0

d²x/dt² + (k/2)x = 0

Multiply both sides by 2!

Edit: Looks like you figured it out while I was typing this.

 

[idir93]

Thanks again