# Finding maximum speed, maximum acceleration, and maximum resisting force for pendulum

1. Mar 14, 2009

### pandaXpress

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

A simple pendulum has a mass of 0.250 kg and a length of 6.00 m. It is displaced through an angle of 10.0° and then released. Solve this problem by using the simple harmonic motion model for the motion of the pendulum.
(a) What is the maximum speed?

(b) What is the maximum angular acceleration?

(c) What is the maximum restoring force?

2. Relevant equations
1$$\stackrel{}{}2$$mv$$^{}2$$ = mgh
this is kinetic energy = potential energy.

3. The attempt at a solution
I tried using the above equation to find maximum speed, but I found that I was getting the wrong answer because I used arc length in the height variable instead of the actual height.
So I guess I'm asking.. how to find height?
Do I use some Pythagorean?
Or just some algebra/trig.. -.-

and also.. what it means "maximum resisting force"?

2. Mar 14, 2009

### pandaXpress

Re: finding maximum speed, maximum acceleration, and maximum resisting force for pend

oops.. the equation is 1/2mv^2 = mgh..
i accidentally did it wrong.. sorry!

3. Mar 14, 2009

### tiny-tim

Welcome to PF!

Hi pandaXpress ! Welcome to PF!
Do what the question says … start with a standard shm equation.
erm … it's restoring force … and they just mean "force"

4. Mar 14, 2009

### pandaXpress

Re: finding maximum speed, maximum acceleration, and maximum resisting force for pend

Hmm.. which shm equation would that be?
My teacher gave us many for different types of waves..
would this be considered a "double open" wave?

so, I would use
v = 2Lf?
and then, where would I use mass or angle?

thanks tiny-tim~~!

5. Mar 14, 2009

### tiny-tim

oooh … no idea what your're talking about …

i thought there was only one shm equation?
shm has force proportional to (minus) distance …

so what's the force in terms of the distance?

6. Mar 14, 2009

### pandaXpress

Re: finding maximum speed, maximum acceleration, and maximum resisting force for pend

ooh, wait is it the equation for velocity on a string?

v = sqrt(FL/m)
so, in this case I guess F (tension) would have to be mass times gravitational force?
and then I could find velocity, right?

7. Mar 14, 2009

### pandaXpress

Re: finding maximum speed, maximum acceleration, and maximum resisting force for pend

Or.. (I just found this on the Internet..)

x(t) = Acos(2 X pi X f X t + phase of oscillation (pi/2, pi/4, etc)

is this that standard one you were talking about?

8. Mar 15, 2009

### tiny-tim

9. Mar 15, 2009

### pandaXpress

Re: finding maximum speed, maximum acceleration, and maximum resisting force for pend

ooh, kay.
I can see from there.

hey, thank you very much~!