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Period of Oscillation

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Question: A second pendulum is suspended from the ceiling of a trolley moving horizontally with an acceleration of 4m/s2. Its period of oscillation is -

a.1.90 seconds
b.1.70 seconds
c.2.30 seconds
d.1.40 seconds

Solution: The complete time taken for a single oscillation is constant and known by the term period. The unit of period of oscillation is measured in seconds (in most cases). The meaning of the term, period defines time spent in an event, irrespective of the repetition. The period of oscillation should demonstrate a periodic motion.

gc = √g2 + a2
=> gc = √102 + 42
=> gc = 10.77 m/seconds

T = 2π √l/gc
=> T = 2π √1/10.77 seconds
=> T = 1.9 seconds
Therefore the correction option is 1.9 seconds, which is option a.

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