Explanation:
An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically. The equation of motion is given by :
[tex]s=6cos\ t+3sin\ t[/tex]
Where
s is in centimeters
t is in seconds
Velocity of the particle, [tex]v=\dfrac{ds}{dt}[/tex]
[tex]v=\dfrac{d(6cos\ t+3sin\ t)}{dt}[/tex]
[tex]v=3cos\ t-6sin\ t[/tex]
Acceleration of the particle, [tex]a=\dfrac{dv}{dt}[/tex]
[tex]v=\dfrac{d(3cos\ t-6sin\ t)}{dt}[/tex]
[tex]v=-6cos\ t-3sin\ t[/tex]
Hence, this is the required solution.
