Answer:
x=0.5 sin 4 t
Explanation:
Given that:
mass m = 4 kg
Stiffness K =64 N/m
Given spring mass system will be in simple harmonic motion.We know that in simple harmonic motion the natural frequency given as follows
[tex]\omega _n=\sqrt{\dfrac{K}{m}}[/tex]
Now by putting the values
[tex]\omega _n=\sqrt{\dfrac{64}{4}}[/tex]
[tex]\omega _n=4 rad/s[/tex]
The equation of SHM given as
[tex]\ddot{x}+\omega _n^2x=0[/tex]
The solution of above equation will be
[tex]x=Asin\omega _nt[/tex]
x=A sin 4 t
Given at t=0 ,V= 2 m/s
So
V= 4 A cos 4 t
2 = 4 A
A= 0.5
The equation of motion will be
x=0.5 sin 4 t
