[western50]

A simple pendulum with mass m = 1.4 kg and length L = 2.76 m hangs from the ceiling. It is pulled back to an small angle of θ = 8.2° from the vertical and released at t = 0, and I figured out the period of oscillation is 3.33s.

1. At t = 0, what is the magnitude of the net force on the pendulum bob? I used newton's second law and it doesn't work

2. What is the maximum speed of the pendulum? I used conservation of energy, I assume it has the maximum energy when the pendulum is at the lowest; but that way of solving is not working

3. What is the angular displacement at t = 3.8 s? (give the answer as a negative angle if the angle is to the left of the vertical) what formula and value should I used for this problem?

4. What is the magnitude of the tangential acceleration as the pendulum passes through the equilibrium position? What is the magnitude of the radial acceleration as the pendulum passes through the equilibrium position?
how can I solve this problem, no idea!

5. Which of the following would change the frequency of oscillation of this simple pendulum?
a. increasing the mass: no because w=sqrt(g/L), mass doesn't matter
b. decreasing the initial angular displacement, no because w=sqrt(g/L), angular displacement is not a variable
c. increasing the length, yes because w=sqrt(g/L), length would change it.
d. hanging the pendulum in an elevator accelerating downward; I think it is yes because gravity is part of the formula of w=sqrt(g/L)

[Unknown008]

Could you show how you got the 3.33s for the period of the oscillation? :confused:

[western50]

It is given in the problem

[Unknown008]

Oh sorry, I must have typed another constant instead of the one I intended to use in my computer calculator... (I miss my calculator :( )

You need to use the formula to get the maximum acceleration of the bob.

You can use:



(at t = 0, a = max, hence cos (wt) = max = 1; there's no need to put phase difference)

You can get A I hope.