If a girl with a mass of 40 kg is swinging from a rope with a length of 2.5 m , then the frequency of her swinging is 0.32 Hz
Simple Harmonic Motion is a motion where the magnitude of acceleration is directly proportional to the magnitude of the displacement but in the opposite direction.
The pulled and then released spring is one of the examples of Simple Harmonic Motion. We can use the following formula to find the period of this spring.
[tex]\large { \boxed {T = 2 \pi\sqrt{\frac{m}{k}} } }[/tex]
T = Periode of Spring ( second )
m = Load Mass ( kg )
k = Spring Constant ( N / m )
The pendulum which moves back and forth is also an example of Simple Harmonic Motion. We can use the following formula to find the period of this pendulum.
[tex]\large { \boxed {T = 2 \pi\sqrt{\frac{L}{g}} } }[/tex]
T = Periode of Pendulum ( second )
L = Length of Pendulum ( kg )
g = Gravitational Acceleration ( m/s² )
Let us now tackle the problem !
Given:
Mass of A Girl = m = 40 kg
Length of Rope = L = 2.5 m
Gravitational Acceleration = g = 10 m/s²
Unknown:
Frequency of Swinging = f = ?
Solution:
Recall the formula for calculating period as mentioned above.
[tex]T = 2 \pi\sqrt{\frac{L}{g}}[/tex]
[tex]T = 2 \pi\sqrt{\frac{2.5}{10}}[/tex]
[tex]T = 2 \pi\sqrt{\frac{1}{4}}[/tex]
[tex]T = 2 \pi \frac{1}{2}[/tex]
[tex]T = \pi ~ seconds[/tex]
[tex]T \approx 3.1 ~ seconds[/tex]
Finally, we can calculate the magnitude of frequency with the following formula.
[tex]f = \frac{1}{T}[/tex]
[tex]f = \frac{1}{\pi} ~ Hz[/tex]
[tex]f \approx 0.32 ~ Hz[/tex]
Grade: High School
Subject: Physics
Chapter: Simple Harmonic Motion
Keywords: Simple , Harmonic , Motion , Pendulum , Spring , Period , Frequency
