s(t)=12+(1/10)cos(12PIt)

Question

The displacement of a particle on a vibrating string is given by the equation  where  is measured in centimeters and  in seconds. Find the velocity of the particle after  seconds.

Give your answer in cm/s. Enter your answer without the units.

Answer 1

s(t)=12+(1/10)cos(12πt),

The image of the specific time doesn't display so let t=1 second:

s(1)=12+0.1cos(12π)=12+0.1cos(6×2π)=12+0.1=12.1 (cm).

Let t=0.25 second, s(0.25)=12+0.1cos(3π)=12-0.1=11.9 (cm).

Velocity = ds/dt=-1.2sin(12πt).

Let t=1 second then velocity=-1.2sin(12π)=0 (cm/s).

Let t=0.25 (¼) second then velocity=-1.2sin(3π)=0 (cm/s).

Let t=0.125 (⅛) second then velocity=-1.2sin(3π/2)=1.2 (cm/s).