Solve Pendulum Problem: Length .76m, Mass .365kg, Angle 12˚

• vinny380
In summary: So, as the bob falls, its gravitational potential energy decreases and its kinetic energy increases. At the lowest point of the swing, all of the potential energy has been converted into kinetic energy. So, to find the bob's speed at that point, you can set the two types of energy equal to each other and solve for v. In summary, the length of the pendulum is .760m with a pendulum bob mass of .365 kg and is released at a 12 degree angle to the vertical. The frequency is .57 and the speed of the bob at the lowest point of the swing can be found by setting the gravitational potential energy equal to the kinetic energy. The total energy stored in the oscillation can be calculated using
vinny380
The length of a simple pendulum is .760m, the pendulum bob has a mass of .365 kg, and it is released at at angle 12 degress to the vertical.
A. Find the frequency. Assume SHM.
B. What is the pendulum bob's speed when it passes through the lowest point of the swing
C. What is the tot al energy stored in this oscilation, assuming no loses.

So A is really easy:
F=(1/2pi)sqrt(9.8/.76)
F= .57

For me, B is the hardest part because I can not find a relevant formula connecting velocity with pendulums. Can anyone advise me how to do this part??

C. I haven't worked on this part yet, but I am ready sure you just have to use the formula E= .5mv^2 +.5kx^2.

Thanks!

vinny380 said:
For me, B is the hardest part because I can not find a relevant formula connecting velocity with pendulums. Can anyone advise me how to do this part??
Consider conservation of mechanical energy.

C. I haven't worked on this part yet, but I am ready sure you just have to use the formula E= .5mv^2 +.5kx^2.
That last term is elastic potential energy--but I don't see any springs in this problem. What other form of energy is relevant here?

Hint regarding B: conservation of energy.

Edit: too late.

so I should use this for B : (1/2)mv2 + (1/2)Iω2 ??

No. What two types of mechanical energy are involved as the pendulum swings?

Potential and Kinetic energy?

Yes, but what kind of potential energy?

mechanical potential energy ?

Here's a hint: What kind of energy changes as the bob rises and falls?

potential and Kinetic

Gravitational potential

1. What is the formula for calculating the period of a pendulum?

The formula for calculating the period of a pendulum is T = 2π√(L/g), where T is the period in seconds, L is the length of the pendulum in meters, and g is the acceleration due to gravity (9.8 m/s^2).

2. How do you determine the length of a pendulum?

The length of a pendulum can be determined by measuring the distance from the point of suspension to the center of mass of the pendulum. In this case, the length is given as .76m.

3. How does the mass of a pendulum affect its period?

The mass of a pendulum does not affect its period. The period of a pendulum only depends on the length and the acceleration due to gravity.

4. Can the angle of the pendulum affect its period?

Yes, the angle of the pendulum can affect its period. However, for small angles (less than 15 degrees), the period is not significantly affected and can be approximated using the small angle approximation formula T = 2π√(L/g).

5. What is the period of a pendulum with the given measurements?

The period of the pendulum can be calculated using the formula T = 2π√(L/g). Plugging in the values of .76m for length and 9.8 m/s^2 for acceleration due to gravity, the period is approximately 1.79 seconds.

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