# What is the total energy stored in this oscillation

1. Jan 29, 2008

### MIA6

1. The length of a simple pendulum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 12-degree to the verticle. (a) With what frequency does it vibrate? Assume SHM. b) What is the pendulum bob's speed when it passes through the lowest point of the swing? c) What is the total energy stored in this oscillation, assuming no losses?

For a), I used the formula f=1/2pai *(g/L)^(1/2) {I can't type the symbol 3.1415.. and radical} I wasn't sure because I didn't use the angle. For b), I used the formula v=radical F/(m/L). I don't think it is right, either, because of the angle. For c) E=1/2mv^2 + 1/2 kx^2, but how do I find x?
Thanks for help.

2. Jan 29, 2008

### Mindscrape

a) I agree

For parts b and c you really need to find the equation of motion. Since you probably are not familiar with differential equations then I will just tell you what it is.

$$x(t) = Acos(\omega t + \delta)$$

Where A and $\delta$ are constants to be determined from your initial conditions, and omega (the w thing) is 2πf. It looks like you are supposed to assume that the pendulum is released from rest i.e. $\frac{dx}{dt}$(0) = 0, and that you are supposed to figure out the initial position x(0), where you would want to use that angle you are worried about.

I know that a lot people teach physics as, formula this, formula that, but try and start from the basics before resorting to formulas.

3. Feb 3, 2008

### MIA6

I know that formula, but first I have to find the amplitude? and it kinda relates to the angle? but you said when x(0)=12 degree which will convert to radians?

4. Feb 3, 2008

### Staff: Mentor

For parts b and c, consider conservation of energy.

5. Feb 3, 2008

### MIA6

Is the speed at the bottom the greatest? But how do I know that at the bottom, it's the equilibrium point? And i don't know the amplitude, either.

6. Feb 3, 2008

### Staff: Mentor

You tell me. Where is PE the lowest?
Equilibrium has nothing to do with it.
What's the initial height of the bob, compared to the lowest point?

7. Feb 3, 2008

### MIA6

Okay. PE is definitely the lowest at bottom because h=0, so the speed is at its maximum. But I don' know the initial height of the bob.

8. Feb 3, 2008

### Staff: Mentor

Good.
Figure it out. You're given the string length and the angle for a reason!

9. Feb 3, 2008

### MIA6

Can I use the formula: x=Lcos(angle)?

10. Feb 3, 2008

### Staff: Mentor

That's almost what you need. That's not the height, but it will help you figure out the height. Draw yourself a diagram.

11. Feb 3, 2008

### MIA6

ehh,, to find the height in triangle?

12. Feb 3, 2008

### Staff: Mentor

Hint: The bottom position is a distance L below the pivot. How far below the pivot is the initial position? (The difference is the change in height.)