Explanation:
Given that,
The mass of the object, m = 0.9 kg
Force constant, k = 170 N/m
Maximum speed of the object, v = 0.2 m/s
Solution,
(a) The angular frequency of the object is given by :
[tex]\omega=\sqrt{\dfrac{k}{m}}[/tex]
[tex]\omega=\sqrt{\dfrac{170}{0.9}}[/tex]
[tex]\omega=13.74\ rad/s[/tex]
The time period is given by :
[tex]T=\dfrac{2\pi}{\omega}[/tex]
[tex]T=\dfrac{2\pi}{13.74}[/tex]
T = 0.45 seconds
(b) The maximum velocity of the object in shm is given by :
[tex]v=A\omega[/tex]
Amplitude,
[tex]A=\dfrac{v}{\omega}[/tex]
[tex]A=\dfrac{0.2}{13.74}[/tex]
A = 0.0145 m
(c) The maximum acceleration of the object is given by :
[tex]a=\omega^2A[/tex]
[tex]a=(13.74)^2\times 0.0145[/tex]
[tex]a=2.73\ m/s^2[/tex]
Therefore, this is the required solution.
