12C Energy n SHM

# 12C Energy n SHM - Announcement Physics 1C Lecture 12C...

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1 Physics 1C Lecture 12C "Fluctuat nec mergitur. = She is swayed by the waves but does not sink." --Motto of the city of Paris Announcement Problem solving sessions: Heemin Kang (TA) Wednesday 8 pm – 9:50 pm, Solis 107 Equations will be given for the quiz – no cheat sheets Simple Pendulum The simple pendulum is another example of simple harmonic motion. Making a quick force diagram of the situation, we find: The tension in the string cancels out with a component of the gravitational force ( mg cos θ ). This leaves only the perpendicular component causing acceleration. Simple Pendulum q = max cos ( w t + f ) In the tangential direction: The length, L, of the pendulum is constant and for small values of : This confirms the form of the motion is SHM !!! The general solution is: Simple Pendulum The angular frequency is The period is The period and frequency depend only on the length of the string and the acceleration due to gravity The period is independent of the mass Pendulum Period All simple pendula that are of equal length and are at the same location (same g ) oscillate with the same period Please note that the period of a pendulum depends on different parameters than the period of a mass-spring system

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2 Pendulum Example A 300g mass on a 30cm long string oscillates as a pendulum. It has a speed of 0.25m/s as
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12C Energy n SHM - Announcement Physics 1C Lecture 12C...

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