The period of vibration of a pendulum varies directly as the square root of the length of the pendulum.

Question

The period of vibration of a pendulum varies directly as the square root of the length of the pendulum. If the period of vibration is 3.6 when the length is 36 inches, find the period when the length is 42.61 inches?

Answer 1

Let L = the Length of the pendulum and P = its period.  If P "varies directly" as the square root of the length, then:

 

P = k√L

 

where k is a constant of proportionality.  To find, k, plug in the known point (P=3.6, L=36) and solve for k:

 

P = k√L

3.6 = k√36

3.6 = k*6

0.6 = k

 

So the equation is:

 

P = (0.6)√L

 

For L = 42.61:

 

P = (0.6)√(42.61)

P = (0.6)(6.53)

P ≅ 3.9 seconds