Modeling Variation

[elizabethj]

Another problem that I can't solve.

The period of a pendulum (the time elapsed during one complete swing of the pendulum) varies directly with the square root of the length of the pendulum. Let T be the period,

be the length of the pendulum, and k an arbitrary constant.

(a) Express this relationship by writing an equation.

The equation I wrote is
T=K(square root L)


(b) To double the period, how would we have to change the length

?

I know that L increases but I don't know by what factor it increases or how to find that out.

Thanks!

 

[Deleted member 4993]

Another problem that I can't solve.

The period of a pendulum (the time elapsed during one complete swing of the pendulum) varies directly with the square root of the length of the pendulum. Let T be the period,

be the length of the pendulum, and k an arbitrary constant.

(a) Express this relationship by writing an equation.

The equation I wrote is
T=K(square root L)


(b) To double the period, how would we have to change the length

?

I know that L increases but I don't know by what factor it increases or how to find that out.

Thanks!

Let the time period be T₁ and the corresponding length be L₁

\(\displaystyle T_1 \ = \ K\sqrt{L_1}\) ....................................... (1)

Let the time period be 2T₁ for double time period and the corresponding length be L₂

\(\displaystyle 2*T_1 \ = \ K\sqrt{L_2}\) ....................................... (2)

Using one in (2)

\(\displaystyle 2*\ K\sqrt{L_1} \ = \ K\sqrt{L_2}\) .........................(3)

Using (3) find \(\displaystyle \dfrac{L_2}{L_1}\)