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

Answer:

Pendulum B

Explanation:

The time period of a pendulum is given by :

$T=2\pi\sqrt{\dfrac{L}{g}}$

Case 1.

Mass, m = 200 g = 0.2 kg

Length of string, l = 1 m

Time, $T_1=2\pi\sqrt{\dfrac{1\ m}{9.8\ m/s^2}}$

T₁ = 2.007 Seconds

Since, $f=\dfrac{1}{T_1}$

$f_1=\dfrac{1}{2.007}$

f₁ = 0.49 Hz

Case 2.

Mass, m = 400 g = 0.4 kg

Length of string, l = 0.5 m

Time, $T_2=2\pi\sqrt{\dfrac{0.5\ m}{9.8\ m/s^2}}$

T₂ = 1.41 seconds

$f₂=\dfrac{1}{T_2}$

$f₂=\dfrac{1}{1.41}$

f₂ = 0.709 seconds

Hence, pendulum B have highest frequency of vibration.