Simple Pendulum Oscillation: Answers and Explanations for Common Test Questions

[Dx]

Hello,

I have two test questions that I missed AT school so i wrote them down. I wanted to know the correct answers as well as a short description of how they came up with that.

1) a simple pendulum consists of a mass attached to a weightless string L. For this system when undergoing small oscillation

a. frequency proportional to amplitude -->that was my original answer
b. period proportional to amplitude
c. frequency independent of mass
frequency is independent of length

My new answer from what I read and understand would be d, am i correct?

2) Simple pendulum A swings back n forth at twice the frequency of a simple pendulum B. what statement is correct?

a. B is twice as long as A
b. B is twice as massive as A
c the length of B is 4 times the length of A
d. the mass of B is 4 times the mass of A

i don't remember but i think the formula is 1/2pi * sqrt(g/L)
anyways can anyone tell me the correct answer and briefly why?

Thanks!
Dx

 

[quantumdude]

Dx, just look up the formulas for the frequency of a physical pendulum. That tells the whole story for #1. As for #2, you got the formula right, so use it to get the answer.

f_A=(1/2π)(g/L_A)^1/2
f_B=(1/2π)(g/L_B)^1/2

You are told that f_A=2f_B

Can you take it from there?

 

[Dx]

Okay!

Ill take it tom. ill let you know how it went, k
Thanks!
dx