L02_a - Simple and Physical Pendula Simple Pendulum: point...

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Unformatted text preview: Simple and Physical Pendula Simple Pendulum: point mass m on massless string L How do we find natural frequency ? o Use Newtons 2 nd law to get differential equation for SHM o Identify from differential equation Forces on hanging mass: o For string at from vertical, sin tangential mg F = Tangential acceleration: o Reminder: for point at distance R from centre of body with angular acceleration 2 2 dt d = , tangential acceleration is R a = tangential o So for mass on string of length L , tangential acceleration is 2 2 tangential dt d L a = (Remember: must be in radians here) Newtons 2 nd Law: tangential tangential ma F = gives 2 2 sin dt d mL mg = o Result: sin 2 2 L g dt d = o Not quite SHM BUT for small angle, sin (for in radians) Simple Pendulum result: for small , have L g dt d = 2 2 o Looks like SHM with L g = 2 Note, does not depend on m ! Strictly SHM for small angle only. Slightly different from sinusoidal for larger amplitude....
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L02_a - Simple and Physical Pendula Simple Pendulum: point...

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