Question

Which would have the highest frequency of vibration? (Prove mathematically.) Pendulum A with a 200 g mass on a 1.0 m string Pendulum B with a 400 g mass on a 0.5 string

Answer 1

Pendulum B

Step-by-step explanation:

The time period of a pendulum is given by :

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

Case 1.

Mass, m = 200 g = 0.2 kg

Length of string, l = 1 m

Time,
`T_1=2\pi\sqrt{(1\ m)/(9.8\ m/s^2)}`

T₁ = 2.007 Seconds

Since,
`f=(1)/(T_1)`

`f_1=(1)/(2.007)`

f₁ = 0.49 Hz

Case 2.

Mass, m = 400 g = 0.4 kg

Length of string, l = 0.5 m

Time,
`T_2=2\pi\sqrt{(0.5\ m)/(9.8\ m/s^2)}`

T₂ = 1.41 seconds

`f₂=(1)/(T_2)`

`f₂=(1)/(1.41)`

f₂ = 0.709 seconds

Hence, pendulum B have highest frequency of vibration.