# String length and period

1. Apr 20, 2005

### dumb

hey,

i have to do an experiment about length of spring and its period, found the relationship, the period is proportional to the square root of the string length. (looks like a pendelum) but i dont understant why when u increase the length, the period increases!! tell me y please! urgent

2. Apr 20, 2005

### misskitty

By increasing the length of the string, you increase the distance the needed to travel. So even though you have not changed the amplitude or the mass at the end of the string it will still take longer to travel that distance. Simply, it takes longer to complete one cycle if it has further to travel if the speed is not changed.

3. Apr 20, 2005

### Werg22

You have to know if the speed stays the same, the force stays same or neither in order to see the relation. But since you say mention squareroot, i'll presume the force is the same.

acceleration 1= acceleration 2
acceleration=v^2/r
v=2*PI*r/T

So
acceleration=(2*PI*r/T)^2/r
=4*PI^2*r^2/T^2r
=4*Pi^2*r/T^2

So

T^2=4*Pi^2*r/a
T=2*PI*r^0.5/a^0.5

So this is the relation with the square root of the radius.

4. Apr 20, 2005

### misskitty

5. Apr 20, 2005

### Werg22

Dumb, if you do it on paper you'll understand better.

6. Apr 22, 2005

### dumb

THANK U SOO MUCH EVERYONE , i did understand!!