Question

13) A pendulum of mass M, length L, amplitude A, and on the earth with acceleration due to gravity of g has a period T. How long would the pendulum need to be in order to to have a period of 2T?

Answer 1

4L

Step-by-step explanation:

mass of pendulum = M, length of pendulum, L1 = L,

acceleration due to gravity = g, Amplitude = A

Use the formula for the time period for simple pendulum

`T = 2\pi \sqrt{(L)/(g)}` ..... (11)

Let the new length be L2 for which the time period is 2T.

`2T = 2\pi \sqrt{(L_(2))/(g)}` ..... (2)

Divide equation (2) by equation (1)

`(2T)/(T) = \sqrt{(L_(2))/(L)}`

So, L2 = 4 L

Thus, the length of the pendulum is 4 L.