Question

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 s = 6 cos(t) + 3 sin(t), t ≥ 0, where s is measured in centimeters and t in seconds. (Take the positive direction to be downward.) (a) Find the velocity and acceleration at time t. g

Answer 1

Step-by-step 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 :

`s=6cos\ t+3sin\ t`

Where

s is in centimeters

t is in seconds

Velocity of the particle,
`v=(ds)/(dt)`

`v=(d(6cos\ t+3sin\ t))/(dt)`

`v=3cos\ t-6sin\ t`

Acceleration of the particle,
`a=(dv)/(dt)`

`v=(d(3cos\ t-6sin\ t))/(dt)`

`v=-6cos\ t-3sin\ t`

Hence, this is the required solution.