Question

A simple pendulum makes 116 complete oscillations in 2.90 min at a location where g = 9.80 m/s².

(a) Find the period of the pendulum.
s

(b) Find the length of the pendulum.
m

Answer 1

a)Number of oscillations = 116

Time=2.9 minutes = 2.9*60 s = 174 seconds.

So, period=(number of oscillation)/time = 116/174=0.6667 seconds.

b)For simple pendulums, T=2*(l/g)^0.5, where T is period, l is length of the pendulum and g is gravitational acceleration.

Here,T=0.6667 seconds

So, 0.6667 = 2*(l/9.8)^0.5

=>l=9.8*[0.6667/(2)]^2 = 0.11 m.