Question

The displacement of a particle on a vibrating string is given by the equation s(t) = 3 + 1 5 sin(3πt) where s is measured in centimeters and t in seconds. Find the velocity of the particle after t seconds.

Answer 1

Answer:

$v(t) = s'(t) = 0+15 (3\pi) cos (3\pi t)\\= 45 \pi co s(3 \pi t)$

Step-by-step explanation:

Given that the displacement of a particle on a vibrating string is given by the equation

s(t) = 3 + 1 5 sin(3πt),

where s is measured in centimeters and t in seconds.

We are find the velocity of the particle at time t.

We know that velocity is nothing but rate of change of s or derivative of s

So

$v(t) = s'(t) = 0+15 (3\pi) cos (3\pi t)\\= 45 \pi co s(3 \pi t)$