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Simple Harmonic Motion - Multiple Choice Questions

Q13. When the length of a simple pendulum is decreased by 600 mm, the period of oscillation is halved. What was the original length of the pendulum?

A 800 mm
B 1000 mm
C 1200 mm
D 1400 mm

T2 = constant x L

we now have to do a bit of manipulation and simple algebra...

T12/L1 = T22/L2

L1= T12L2 /T22

L1 = L

L2 = L - 600

T1 = T

T2 = 0.5 T

L = T2(L - 600)/(0.5 T)2

L = 4(L - 600)

3L = 2400

L = 800 mm

(and therefore length of the second was 200 mm)

Double check

root 800 = 28.28

root 200 = 14.14 (half the value)