2 oscillations in 5 seconds, so
frequency per second = 2/5
⇒ frequency per second = 0.4 Hz
Hence, frequency of oscillation = 0.4 hertz.
As we know,
Time Period (T) = 1/f
So, substituting the value of f = 0.4 hertz, in the equation above we get,
Time Period (T) = 1/0.4
⇒ T = 2.5 s
Hence, time period of the pendulum is 2.5 s
(b) As we know,
T = 2 \pi \sqrt{l\over g}
Given,
g = 9.8 ms-2
and we know,
π = 3.14
T = 2.5 s
Substituting the values in the formula above we get,
2.5 = 2 × 3.14 × \sqrt {l\over9.8}
⇒ ({2.5\over2 \times 3.14})={\sqrt {l\over9.8}}
⇒ ({2.5\over 6.28})^2={l\over9.8}
⇒ (0.398)^2={l\over9.8}
⇒ 0.158={l\over9.8}
⇒ l = 9.8 × 0.158 = 1.55
Hence, the length of a seconds’ pendulum = 1.55 m