Frequency of an oscillating mass with springs in series

[laurette1029]

Homework Statement

A block on a frictionless table is connected as shown in the figure to two springs having spring constants k1 and k2.

Find an expression for the block's oscillation frequency f in terms of the frequencies f1 and f2 at which it would oscillate if attached to spring 1 or spring 2 alone.
Give your answer in terms of f1 and f2.

Homework Equations

f=(1/2pi)*sqrt(k/m)

The Attempt at a Solution

If the object was attached to spring 1 alone, the frequecy would be:

f1=(1/2pi)*sqrt(k1/m)

If the object was attached to spring 2 alone, the frequecy would be:

f2=(1/2pi)*sqrt(k2/m)

Since the two springs are in a serie, the constant k of the system of spring is :

1/k1+1/k2=1/k which means k=k1k2/k1+k2

Then the frequecy of the system of springs should be f=(1/2pi)*sqrt(k1k2/m(k1+k2))

This is where I get stuck, I don't know how to express f in terms of f1 and f2.

 

[PeterO]

Homework Statement

A block on a frictionless table is connected as shown in the figure to two springs having spring constants k1 and k2.

Find an expression for the block's oscillation frequency f in terms of the frequencies f1 and f2 at which it would oscillate if attached to spring 1 or spring 2 alone.
Give your answer in terms of f1 and f2.

Homework Equations

f=(1/2pi)*sqrt(k/m)

The Attempt at a Solution

If the object was attached to spring 1 alone, the frequecy would be:

f1=(1/2pi)*sqrt(k1/m)

If the object was attached to spring 2 alone, the frequecy would be:

f2=(1/2pi)*sqrt(k2/m)

Since the two springs are in a serie, the constant k of the system of spring is :

1/k1+1/k2=1/k which means k=k1k2/k1+k2

Then the frequecy of the system of springs should be f=(1/2pi)*sqrt(k1k2/m(k1+k2))

This is where I get stuck, I don't know how to express f in terms of f1 and f2.

Perhaps you need to use proportion to get rid of a lot of the clutter.

f1=(1/2pi)*sqrt(k1/m) = (1/2pi)*sqrt(1/m)*sqrt(k1) = A*k1
f2=(1/2pi)*sqrt(k2/m) = (1/2pi)*sqrt(1/m)*sqrt(k2) = A*k2

I replaced all those constant/equal bits with the symbol A. The was no significance in me choosing A, I could have used any letter/symbol - except the ones already used as that would be confusing [so m is out of the question]

When you do a similar thing to the combined spring situation you may find something.