Question

A simple pendulum is constructed by hanging a heavy ball by 5.0 m long string. It undergoes small oscillations. (a) How many oscillations does it make per second? (b) What will be the frequency if the system the system is taken on the moon where the acceleration due to the gravitation of the moon is 1.67 m/s²?

Answer 1

Given, Length of the pendulum = 5 m.

(a). $T = 2\pi \frac{l}{g}$

Thus, T = 2 × 22/7 × √(5/9.8)

∴ T = 4.49 seconds.

Thus, Frequency(f) = 1/4.49

= 0.222 s⁻¹

(b). At moon, g = 1/6 × 9.8 = 1.63 m/s².

Thus,

$T = 2\pi \frac{l}{g}$

∴  T =  2 × 22/7 × √(5/1.67)

∴ T = 10.99 seconds.

Thus, frequency(f) = 1/T

= 0.09 s⁻¹.

Hope it helps.

Answer 2

Answer:

Given, Length of the pendulum = 5 m.

(a).

Thus, T = 2 × 22/7 × √(5/9.8)

∴ T = 4.49 seconds.

Thus, Frequency(f) = 1/4.49

= 0.222 s⁻¹

(b). At moon, g = 1/6 × 9.8 = 1.63 m/s².

Thus,

∴  T =  2 × 22/7 × √(5/1.67)

∴ T = 10.99 seconds.

Thus, frequency(f) = 1/T

= 0.09 s⁻¹.