Question

A simple pendulum is swinging back and forth through a small angle, its motion repeating every 1.07 s. How much longer should the pendulum be made in order to increase its period by 0.25 s?

Answer 1

initial time period, T1 = 1.07 s

let L1 is the initial length of the pendulum,

we know, T1 = 2*pi*sqrt(L1/g)

T1^2 = 4*pi^2*L1/g

==> L1 = T1^2*g/(4*pi^2)

= 1.07^2*9.8/(4*pi^2)

= 0.2842 m

new time period, T2 = 1.07 + 0.25

= 1.32 s

let L2 is the new length of the time period.

we kmow, L2 = T2^2*g/(4*pi^2)

= 1.32^2*9.8/(4*pi^2)

= 0.4325 m

increase in length od the pendulum = L2 - L1

= 0.4325 - 0.2842

= 0.148 m (or) 14.8 cm <<<<<<<--------------Answer