Hey, just starting my new physics course this semester and to start we are revie
ID: 1705336 • Letter: H
Question
Hey, just starting my new physics course this semester and to start we are reviewing some older material from the first physics course (I'm in PHY 213 and the 1st one was 211). I haven't taken a physics course in 2 years (since the first time I took it was very discouraging...) so I'm needing a bit of help with a problem or two. Here it is:a) If a mass of 2kg is attached to a string of length 1m and pulled back to the angle shown (30 degrees from straight down), what velocity will the mass have at the "bottom" of its swing?
b) What will the period of its oscillations be?
This is one of 4 questions and I've managed to figure the other 3 out with reviewing a bunch of the old material in my spare time. This is due Wednesday and I'm still at a loss how to do it. I posted this question here earlier but it wasn't answered. I'm looking through my book and there isn't really a related question to help me work through it although I believe this question has something to due with centripetal acceleration on the string since it is under constant acceleration (I'm assuming) and therefore has a constant tension in the string but the book hasn't been able to help me very much. Any help would be appreciated! Thanks!
Explanation / Answer
The angular frequency w of a simple pendulum with small amplitude is w = (k/m)^1/2 = [(m * g/L)/m]^1/2 = (g/L)^1/2 The corresponding frequency and period relations are f = (w/2pi) = (1/2pi) * (g/L)^1/2 and T = (2pi/w) = (1/f) = 2pi * (L/g)^1/2 The velocity of pendulum is given by v = A * w * sin(wt) when wt = 90o we have v_max = A * w where A is amplitude of oscillations