A simple pendulum is kept suspended vertically in a stationary bus. The bus starts moving with an acceleration $a$ towards the left (Figure 5.143). As observed inside the bus (neglect friction, size of ball very small):

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In the bus frame g e ff ​ = a 2 + g 2 ​ and the equilibrium is tilted tan − 1 ( a / g ) . The bob starts from the vertical, so the angular amplitude is tan − 1 ( a / g ) for any a . The simple period formula needs a small amplitude, i.e. a ≪ g .

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