The amplitude of its simple harmonic motion is about 0.37 m
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<h3>Further explanation</h3>
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.
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
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.
![\large{\boxed{T = 2 \pi\sqrt{\frac{m}{k}}}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cboxed%7BT%20%3D%202%20%5Cpi%5Csqrt%7B%5Cfrac%7Bm%7D%7Bk%7D%7D%7D%7D)
T = Periode of Spring ( second )
m = Load Mass ( kg )
k = Spring Constant ( N / m )
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
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.
![\large{\boxed{T = 2 \pi\sqrt{\frac{L}{g}}}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cboxed%7BT%20%3D%202%20%5Cpi%5Csqrt%7B%5Cfrac%7BL%7D%7Bg%7D%7D%7D%7D)
T = Periode of Pendulum ( second )
L = Length of Pendulum ( kg )
g = Gravitational Acceleration ( m/s² )
Let us now tackle the problem !
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<u>Given:</u>
displacement = x = 0.30 m
kinetic energy = ½ × potential energy
<u>Asked:</u>
amplitude = A = ?
<u>Solution:</u>
We will use conservation of energy as follows:
![U_{max} = U + K](https://tex.z-dn.net/?f=U_%7Bmax%7D%20%3D%20U%20%2B%20K)
![\frac{1}{2}k A^2 = U + \frac{1}{2}U](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dk%20A%5E2%20%3D%20U%20%2B%20%5Cfrac%7B1%7D%7B2%7DU)
![\frac{1}{2}k A^2 = \frac{3}{2}U](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dk%20A%5E2%20%3D%20%5Cfrac%7B3%7D%7B2%7DU)
![\frac{1}{2}k A^2 = \frac{3}{2}( \frac{1}{2}kx^2 )](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dk%20A%5E2%20%3D%20%5Cfrac%7B3%7D%7B2%7D%28%20%5Cfrac%7B1%7D%7B2%7Dkx%5E2%20%29)
![A^2 = \frac{3}{2} x^2](https://tex.z-dn.net/?f=A%5E2%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20x%5E2)
![A^2 = \frac{3}{2} \times 0.30^2](https://tex.z-dn.net/?f=A%5E2%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%5Ctimes%200.30%5E2)
![A^2 = 0.135](https://tex.z-dn.net/?f=A%5E2%20%3D%200.135)
![A = \sqrt{0.135}](https://tex.z-dn.net/?f=A%20%3D%20%5Csqrt%7B0.135%7D)
![A \approx 0.37 \texttt{ m}](https://tex.z-dn.net/?f=A%20%5Capprox%200.37%20%5Ctexttt%7B%20m%7D)
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<h3>Learn more</h3>
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<h3>Answer details</h3>
Grade: High School
Subject: Physics
Chapter: Simple Harmonic Motion
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
Keywords: Simple , Harmonic , Motion , Pendulum , Spring , Period , Frequency
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