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

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, $v=\dfrac{ds}{dt}$

$v=\dfrac{d(6cos\ t+3sin\ t)}{dt}$

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

Acceleration of the particle, $a=\dfrac{dv}{dt}$

$v=\dfrac{d(3cos\ t-6sin\ t)}{dt}$

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

Hence, this is the required solution.