Answer:
The equation which describes the simple harmonic motion is [tex]x=0.5\cos(15.81t)[/tex]
Explanation:
Given that,
Mass = 0.4 kg
Spring constant = 100 N/m
Maximum displacement = 0.5 m
We need to calculate the angular frequency
[tex]\omega=\sqrt{\dfrac{k}{m}}[/tex]
[tex]\omega=\sqrt{\dfrac{100}{0.4}}[/tex]
We need to find the equation which describes the simple harmonic motion
Using equation of simple harmonic motion
[tex]x = A\cos\omega t[/tex]
Where, A = amplitude
[tex]\omega [/tex] = angular frequency
Put the value of angular frequency
[tex]x=A\cos\sqrt{\dfrac{k}{m}t}[/tex]
Put the value in the equation
[tex]x=0.5\cos\sqrt{\dfrac{100}{0.4}t}[/tex]
[tex]x=0.5\cos(15.81t)[/tex]
Hence, The equation which describes the simple harmonic motion is [tex]x=0.5\cos(15.81t)[/tex]
