Why does the period increase when the string length is increased?

[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 don't understant why when u increase the length, the period increases! tell me y please! urgent

 

[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.

 

[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.

 

[misskitty]

Nice mathematical explanation! Dumb, does that help you?

 

[Werg22]

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

 

[dumb]

THANK U SOO MUCH EVERYONE , i did understand!