What is the comparison of the formula for the period of a pendulum to the equation of a line, y=mx + c?

Greyson Landry
2022-07-16
Answered

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Bradley Sherman

Answered 2022-07-17
Author has **17** answers

Relationship between time period (T) and length (L) of the string of a pendulum is given as, $T=2\pi \sqrt{\frac{L}{g}}$ (where g is acceleration due to gravity on earth)

So,we can write, $T=2\frac{\pi}{\sqrt{g}}\sqrt{L}$

Now,compare this with y=mx

So, Graph of T vs. $\sqrt{L}$ will be a straight line passing through origin,where slope$=\mathrm{tan}\theta =2\frac{\pi}{\sqrt{g}}$

So,we can write, $T=2\frac{\pi}{\sqrt{g}}\sqrt{L}$

Now,compare this with y=mx

So, Graph of T vs. $\sqrt{L}$ will be a straight line passing through origin,where slope$=\mathrm{tan}\theta =2\frac{\pi}{\sqrt{g}}$

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A string is made to vibrate at its third harmonic. The diagram shows two points P and Q at a particular instant in time. Which of the following compares the period of vibration of P and Q?

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(The string is closed at both ends; P is just before the first maximum antinode and Q is at the next minimum antinode).

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B. Period of P and Q is different

Why is it A not B?

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