What does frequency depend on?

Classical Mechanics Level 3

Two objects of mass $5 \text{ kg}$ and $20\text{ kg}$ are attached to a spring with a spring constant $k$ (in Newtons per meter) and length $l$ meters.

The angular frequency of the oscillation of this system when the spring is compressed by a force $F$ Newtons and then released is given by $ak^bl^cF^d$ , where $a, b, c$ , and $d$ are constants.

Find $a+b+c+d$ .

The answer is 1.

1 solution

Dallin Richards
Jan 28, 2017

Walter Lewin does a good job explaining the idea of an "equivalent spring constant" here: https://www.youtube.com/watch?v=mE6lQCdzb1M Alternatively, you could also think of an equivalent mass, usually called the reduced mass, where like the equivalent spring constant, you take the harmonic sum of the masses.

That's cool. So just take the easily derived result from the 1-mass-1-spring case ( $\sqrt{\frac{k}{m}}$ ). Then calculate the equivalent single mass as the product over the sum of the two masses (yielding 4 kg). Then you get $\frac{1}{2} k^{\frac{1}{2}} l^0 F^0$ . So $a+b+c+d = \frac{1}{2} + \frac{1}{2} + 0 + 0 = \boxed{1}$ .

Steven Chase - 4 years, 4 months ago

What does frequency depend on?

The answer is 1.

1 solution

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