Use V=Voe^-t/RC and T=RC to derive T1/2=Tln2
1 answer:
Enclosed is some guidance algebra.I find this q a little confusing. It quotes "RC" which usually makes me think of electrical circuits and time constants based on converting calculating RC value and equating that to t for one time constant then 2RC for two time constants etc. The theory being that after 5 time constants - 5RC - a circuit is stable. BUT, this q then goes on to mention HALF LIFE. The curves for both half life and time constant are both exponential, as in the number e to the power of something, but the algebra is slightly different. I hope my algebra is ok.
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Answer:
<em>The new period of oscillation is D) 3.0 T</em>
Explanation:
<u>Simple Pendulum</u>
A simple pendulum is a mechanical arrangement that describes periodic motion. The simple pendulum is made of a small bob of mass 'm' suspended by a thin inextensible string.
The period of a simple pendulum is given by
Where L is its length and g is the local acceleration of gravity.
If the length of the pendulum was increased to 9 times (L'=9L), the new period of oscillation will be:
Taking out the square root of 9 (3):
Substituting the original T:
The new period of oscillation is D) 3.0 T