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djverab [1.8K]
4 years ago
9

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 rel

eased, 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
Physics
1 answer:
GrogVix [38]4 years ago
6 0

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.

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