# Frequency of spring

1. Apr 18, 2012

### jsmith613

1. The problem statement, all variables and given/known data

look at attachment

2. Relevant equations

3. The attempt at a solution
so we know that the frequency of a spring is given by
$f = \frac{1}{2 pi} \sqrt{\frac{k}{m}}$

so the answer should be A
BUT the answer is C. why?

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2. Apr 18, 2012

### collinsmark

Why do you think the answer should be A? How would adding an inelastic string affect the variables described by the
$$f = \frac{1}{2 \pi} \sqrt{\frac{k}{m}}$$
equation?

3. Apr 19, 2012

### jsmith613

surely it affects spring consttant?

4. Apr 19, 2012

### jsmith613

how does changing the length of the spring change k??
although F = kx
F/x is constant for a particualr string

5. Apr 19, 2012

### PeterO

A strong spring will be extended a small amount when a load m is attached.
A weak spring will be extended a large amount when a load m is attached.

Suppose the original spring was extended 10cm by the load m
That means each half was extended 5 cm by the load m.

Thus in example C, the load m extends the piece of spring only 5cm. the half spring behaves as a stronger spring that the whole spring.

In example D, each of the springs will be extended 10cm by the load - so a total extension of 20cm. The double spring behaves as a weaker spring than a single spring.

6. Apr 19, 2012

### jsmith613

so basically I have to know that a shorter spring is stiffer than a longer spring?

7. Apr 19, 2012

### PeterO

To say that short springs are stiffer than long springs is not strictly correct.
I think you will find that the 30 cm spring from the front suspension of a car is much stiffer than the 10cm spring in a laboratory "spring balance"

Instead, you have to note that when a spring is stretched by a load, a fraction of that spring stretches only a fraction of that amount.

When that is applied to compute a spring constant, it means that if you have two sections of the same original spring, the shorter section will have a higher spring constant.

When you study materials, you will come across the concept of Young's Modulus. That is a measure that is used to show that two samples have basically the same material properties, despite the fact that one of them is extended more in an absolute sense.

8. Apr 19, 2012

cheers