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

Pendulum B

Explanation:

The time period of a pendulum is given by :

Case 1.

Mass, m = 200 g = 0.2 kg

Length of string, l = 1 m

Time,

T₁ = 2.007 Seconds

Since,

f₁ = 0.49 Hz

Case 2.

Mass, m = 400 g = 0.4 kg

Length of string, l = 0.5 m

Time,

T₂ = 1.41 seconds

f₂ = 0.709 seconds

Hence, pendulum B have highest frequency of vibration.