Question

Tom has two pendulums with him. Pendulum 1 has a ball of mass 0.2 kg attached to it and has a length of 5 m. Pendulum 2 has a ball of mass 0.6 kg attached to a string of length 1 m. How does mass of the ball affect the frequency of the pendulum

Answer 1

Step-by-step explanation:

Given:

Pendulum 1:

Mass, m = 0.2 kg

Length, l = 5 m

Pendulum 2:

Mass, m = 0.6 kg

Length, l = 1 m

Period, T = 2pi × sqrt(l/g)

Note:

Frequency, f = 1/T

Mass is not a parameter in the formula for calculating frequency of the pendulum. Therefore, mass does not affect the frequency of the motion.

Let's find the frequency of both pendulum irrespective of their masses.

T1 = 2pi × sqrt(5/9.8)

= 4.488 s

Frequency, f1 = 0.22 Hz

T2 = 2pi × sqrt(1/9.8)

= 2.007 s

Frequency, f1 = 0.498 Hz

= 0.5 Hz

Answer 2

Given Information:

Pendulum 1 mass = m₁ = 0.2 kg

Pendulum 2 mass = m₂ = 0.6 kg

Pendulum 1 length = L₁ = 5 m

Pendulum 2 length = L₂ = 1 m

Required Information:

Affect of mass on the frequency of the pendulum = ?

Answer:

The mass of the ball will not affect the frequency of the pendulum.

Step-by-step explanation:

The relation between period and frequency of pendulum is given by

f = 1/T

The period of pendulum is given by

T = 2π√(L/g)

Where g is the acceleration due to gravity and L is the length of the string

As you can see the period (and frequency too) of pendulum is independent of the mass of the pendulum. Therefore, the mass of the ball will not affect the frequency of the pendulum.

Bonus:

Pendulum 1:

T₁ = 2π√(L₁/g)

T₁ = 2π√(5/9.8)

T₁ = 4.49 s

f₁ = 1/T₁

f₁ = 1/4.49

f₁ = 0.22 Hz

Pendulum 2:

T₂ = 2π√(L₂/g)

T₂ = 2π√(1/9.8)

T₂ = 2.0 s

f₂ = 1/T₂

f₂ = 1/2.0

f₂ = 0.5 Hz

So we can conclude that the higher length of the string increases the period of the pendulum and decreases the frequency of the pendulum.