Question

What are the period P and frequency T of oscillation of a pendulum of length one half​ft? (Hint: Upper P equals 2 pi StartRoot StartFraction Upper L Over 32 EndFraction EndRoot​,where L is the length of the pendulum in feet and the period P is in​ seconds.)

Answer 1

Answer:

$P'=P \sqrt{\dfrac{1}{2}}$

T ' = √2 T

Step-by-step explanation:

Given that

Time period = P

Frequency = T

We know that time period for pendulum given as

$P=2\pi \sqrt{\dfrac{L}{g}}$

When the length become half then time period will become p'

L'=L/2

$P'=2\pi \sqrt{\dfrac{L'}{g}}$

$P'=2\pi \sqrt{\dfrac{L}{2g}}$

$P'=P \sqrt{\dfrac{1}{2}}$

It means that time period will become 0.707 P.

We know that frequency T

T= 1 /P

T'  = 1/P'

T'=√2/P

T ' = √2 T