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## AP®︎/College Physics 1

### Course: AP®︎/College Physics 1>Unit 8

Lesson 3: Simple pendulums

# Pendulums

David explains how a pendulum can be treated as a simple harmonic oscillator, and then explains what affects, as well as what does not affect, the period of a pendulum. Created by David SantoPietro.

## Want to join the conversation?

• We do not take gravity into account in case of spring but we do in case of pendulum.Why is it like that?
• If you are talking about horizontal spring then it is coz we are talking about horizontal forces and gravity acts vertically. Force of gravity, in that case, is actually equal to normal acting on the mass, & it has nothing to do with horizontal forces (moving mass left & right).
But... In the case of a pendulum, gravity (still) acts vertically but, in this case, it helps it to move as David explained!!
• can u give me mathmatical reason why pendulum is not a shm in larger angles?
• If you study the derivation of the motion of the pendulum, at some point the angle is assumed to be small so that the angle (measued in radians) is equal to the sine of the angle. This is true only for small angle and therefore small displacement

A = tan A = sin A for small A
• why does restoring force in a pendulum depend upon gravity
• without gravity, there would be no force to bring it back to its rest position.
The bigger the gravitational field strength, the bigger will be the restoring force.

OK??
• Why does mass not change the time period of the pendulum?
• another way to understand that concept is.....think...two balls of different mass are left from same height...if there isnt any air resistance....which one will come first?......Obviously both will land together. Gravitational force produces same acceleration on every body. As oscillation of pendulum depends upon gravity, length of the string and angle from which it is left......mass has no role...
• If we want the exact period for a pendulum swinging with larger angles (70 degress for example), how would I adjust the formula so I get the exact answer and not just an approximation?
• If you were to try and derive the period of the pendulum (which involves setting up differential equations), you eventually get this term, sin(θ), which makes the whole differential equation unsolvable. To alter this differential equation into a solvable one, you can write sin(θ) ≈ θ via the small-angle approximation (while sacrificing a bit of accuracy).

This bottleneck is the very reason why the period formula works best when θs are smallest; if you were to look at the graphs of y=sin(x) and y=x, they are closest to each other the smaller x is (thus more accurate), and farther with bigger x values.

Therefore, as of right now, there is no absolute solution to your question. However, there are methods of approximating unsolvable differential equations (Euler's method, for example), that can get much closer to the exact answer than would the traditional period formula.

(I'm sorry, as typing out differential equations would be tedious. However, here is a link to the derivation: http://web.mit.edu/18.098/book/extract2009-01-16.pdf)
• Can you explain using torque equations why the Amplitude does not affect the Period? Thanks
• Can someone direct me to the 'awesome derivation' of the equation at ? (I know calculus)
• Why the time period of the pendulum does not depend on the displacement of the angle theta?
• because the average speed of the pendulum goes up together with the distance that the pendulum has to travel.