Question

The time period, T, of a simple pendulum is directly proportional to the square root of the length, d, of the pendulum.

When d=6, T=5

Find the value of T when d=3

Input note: give your answer correct to 2 decimal place.

Answer 1

Answer: T= 3.54

Explanation:

Step 1

Given that

The time period, T, s doirectly proportional to the square root of the length, d, of the pendulum, we have that

T ∝
`√(d)`

Introducing the constant of proportionality, we have that

T= K
`√(d)`.

Step 2

When d=6, T=5, K =?

T= K
`√(d)`.

5 = k
`√(6)`

5= k x 2.44949

k =5/2.44949

k =2.041

Therefore, when d = 3 , T= ?

T= K
`√(d)`

T= 2.041 x
`√(3)`

T= 3.53511≈ 3.54