# Simple Pendulum: Amplitude, velocity, and angular position.

1. Apr 12, 2012

### howsockgothap

θθ1. The problem statement, all variables and given/known data

A simple pendulum of mass 20.0 g is suspended by a length of string 1.0 m. It is pulled from equilibrium so that it's raised 10.0 cm and released. Angular position given by θ(t)=θmaxcos(ωt+∅)

What is the period? What is the maximum velocity of the pendulum? What is the phase constant if the mass passes through its lowest point at t=0?

2. Relevant equations

θ(t)=θmaxcos(ωt+∅)
v0=ωA

3. The attempt at a solution
I found T using gravity and length and am trying to get maximum velocity. My confusion stems mostly from the fact that our professor only discussed acceleration in terms of pendulums and then very briefly.

I thought that I could use v=ωA but I'm a little confused about how I'm supposed to get A for the pendulum, can I just plug in Lsinθ?

For the last part it seems to me I can just use θ=θmaxcos(∅) since t=0, but then I get caught up on what to plug in for θ. It's at its lowest point, so it seems I should simply plug in 0 and am then left with 0=θmaxcos(∅). How do I get θmax? I'm guessing this is tied in to my difficulties with part 2.

2. Apr 12, 2012

### OldEngr63

You need to write F = m a for the pendulum bob, remembering that there is motion in two directions. This can be done in x & y, or you can do it in r and theta (if you have talked about polar coordinates); either way should get you to the same final result.

I'm not sure what you mean by the quantity V sub o; what is your definition for this?

3. Apr 12, 2012

### howsockgothap

V sub o was velocity, but that is not something I'm sure of, only a wild guess based on equations in our text because our prof didn't discuss this.

4. Apr 12, 2012

### OldEngr63

The V almost certainly represents a velocity, but the subscript o usually denotes a particular time, often time t = 0, but not always.

I'd bet that your prof expects you to READ the book, not just look at the pictures and equations. That would be almost like listening to more lecture, and it would cover more ground. Try it; you may like it.

5. Apr 12, 2012

### howsockgothap

Hey man, as much as I appreciate the passive agressive insult, I have, unbelievably, read the book. Several times, in fact. I obviously still don't understand it, which is why I went here for help.