Answer :
For a pendulum with a massless rope 'L' meters long, swinging through
a small arc, the period of the swing is
2 π √(L/g) seconds .
and it doesn't depend on the mass of the thing on the end of the rope ...
that could be a pebble or a bus.
For the girl on the 2.5-m rope,
Period = (2 π) √(2.5 / 9.8) = 3.17 seconds
Frequency = 1 / period = about 0.315 Hz .
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
Further explanation
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]
Learn more
- Model for Simple Harmonic Motion : https://brainly.com/question/9221526
- Force of Simple Harmonic Motion : https://brainly.com/question/3323600
- Example of Simple Harmonic Motion : https://brainly.com/question/11892568
Answer details
Grade: High School
Subject: Physics
Chapter: Simple Harmonic Motion
Keywords: Simple , Harmonic , Motion , Pendulum , Spring , Period , Frequency
