What is the fundamental period for this pendulum?

Question

Hello,

 

I'm taking a summer course in college physics and am reviewing some practice questions to prepare for my oncoming exam. I'd really appreciate some help on this question that I'm not sure about.

 

Question: There are two kinds of motion involved with a two ton mass (2000 kg) hanging from a string. The string has a amass of 5 kg with a length of 100 meters. What is the period of the pendulum? What is the period of the fundamental?

 

I calculated the period to be about 20 seconds with the T=2pi • sqrt L/g formula but I'm not sure about the "period of the fundamental." 

 

Thanks in advance for any assistance. 

Answer 1

Hi Katelyn, what you have here is a simple harmonic oscillator. What you actually solved for is the period of the fundamental. The fundamental is the time it takes for one cycle of the pendulum to complete. The equation you used T=2*pi*sqrt(L/g)= 28.1 seconds gives you the fundamental period. The period of the pendulum is 28.1*n where n is a whole integer amount of the fundamental which is usually described at the harmonic number(n). The harmonic number(n) of the 1st harmonic is commonly called the fundamental in simple harmonic motion.