The velocity of an object in simple harmonic motion is given by v(t)= -(0.275 m/s)sin(23.0t + 2.00π), where t is in seconds.

Question

1) What is the first time after t=0.00 s at which the velocity is -0.100 m/s?
2) What is the object's position at that time?

I tried solving for time and got -13.019 which is wrong :(. It can't even be negative so I don't know what to do.

Answer 1

Remember it is the same at the same time every period.(every 2pi inside the sine function so forget the 2 pi in there.)
Now from t = 0 to 23t = 2 pi is a period so
period T = 2 pi/23 = .273 seconds

v(t)= -(0.275 m/s)sin(23.0t + 2.00π)
-.1 = -(0.275 m/s)sin(23.0t)
sin 23 t = .364
23 t = .372 rad
t = .0162 seconds

Answer 2

Thanks, I see how it's done. For question 2, I did: x = dv/dt = 0.275*cos(23t) = 0.275*cos(0.372rad) = 0.256 m which is incorrect for some reason.