The position of a 50 g oscillating mass is given by 𝓍(t) = (2.0 cm) cos (10 t ─ π/4), where t is in s. Determine: h. The velocity at t = 0.40 s.

Video transcript

Hey, everyone. So this problem is dealing with simple harmonic motion. Let's see what it's asking us. The equation X of T equals five centimeters multiplied by the sine of eight T plus pi over three where T is in seconds represents the displacement of a g mass. What will be the velocity of the mass at T equals 0.35 seconds. If it is oscillating, our multiple choice answers here are a negative 34 centimeters per second. B 34 centimeters per second. C negative 30.4 centimeters per second or D 30.4 centimeters per second. OK. So this problem is pretty straightforward as long as we recall that the derivative of position is velocity. So they give us the position equation and starts this X of T equals five centimeters multiplied by the sign of eight plus pi divided by three. And so we can recall that D X D T is the same as V of T. In other words, the derivative of position or X is velocity. And so we'll take the derivative of this equation. And so we come out with five centimeters multiplied by eight, multiplied by the cosine of eight plus pi divided by three. And then they're asking us for the velocity at time equals 0. seconds. So we'll plug in 0.35 seconds for time. And so that velocity we're going to have centimeters multiplied by the cosine of eight, multiplied by 0.35 seconds plus I divided by three. And we plug that into our calculator and we get negative 30.4 centimeters per second. And so that is the answer for this problem and that aligns with answer choice. C so that's all we have for this one. We'll see you in the next video.