Question

Which would have the highest frequency of vibration? Why? Prove
mathematically.
Pendulum A: A 200-g mass attached to a 1.0-m length string
Pendulum B: A 400-g mass attached to a 0.5-m length string​

Answer 1

Answer:

Pendulum B has a higher frequency of vibration (0.450 Hz) compared to Pendulum A (0.318 Hz).

what is a frequency?

Frequency refers to the number of cycles or oscillations that occur per unit of time. In physics, it is defined as the number of complete waves or vibrations that occur in one second and is measured in units of Hertz .

Explanation :

The frequency of vibration of a pendulum depends on its length and acceleration due to gravity. It can be calculated using the formula:

f = (1/2π) x √(g/L)

Where,

f = frequency of vibration (in Hz)

g = acceleration due to gravity (9.81 m/s^2)

L = length of the pendulum (in meters)

Using this formula, we can calculate the frequencies of vibration for Pendulum A and Pendulum B and compare them to determine which one has the higher frequency.

For Pendulum A:

L = 1.0 m

m = 0.2 kg

fA = (1/2π) x √(g/L)

fA = (1/2π) x √(9.81/1.0)

fA = 0.318 Hz

For Pendulum B:

L = 0.5 m

m = 0.4 kg

fB = (1/2π) x √(g/L)

fB = (1/2π) x √(9.81/0.5)

fB = 0.450 Hz

Therefore, Pendulum B has a higher frequency of vibration (0.450 Hz) compared to Pendulum A (0.318 Hz).

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Answer 2

Answer:

The pendulum B with the ( 400-g mass attached to a 0.5-m length string​) will have the highest frequency of vibration, the reason has been explained.

Explanation:

The frequency of vibration of a pendulum depends on its length and the acce leration due to gravity, as shown by the formula:

f = 1/2π √(g/L)

where f is the freq. of vibration, g is the acceleration due to gravity, and L is the length of the pendulum.

Using this formula, we can calculate the frequencies of vibra tion for the two pendulums:

For Pendulum A:

f = 1/2π √(g/L)

f = 1/2π √(9.81 m/s^2 / 1.0 m)

f = 1.66 Hz

For Pendulum B:

f = 1/2π √(g/L)

f = 1/2π √(9.81 m/s^2 / 0.5 m)

f = 2.21 Hz

Therefore, Pendulum B has a higher frequency of vibrati on than Pendulum A.

This is because the frequency of vibration is inversely proportional to the length of the pendulum, and directly proportional to the square root of the acceleration due to gravity. Pendulum B has a shorter length and the same acceleration due to gravity as Pendulum A, which means it will have a higher frequency of vibration. This can also be seen from the formula, as the square root of 1/2L is larger for Pendulum B than Pendulum A, resulting in a higher frequency of vibration.

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