Question

A simple pendulum is swinging back and forth through a small angle, its motion repeating every 1.06 s. How much longer should the pendulum be made in order to increase its period by 0.32 s?

Answer 1

Answer:

The pendulum should be made longer by 0.194m in order to increase its period by 0.32s

Explanation:

using the formula T= 2π$\sqrt{\frac{L}{g} }$

rearranging the equation and making L subject of formula we have;

L=T²g/4π²

lets calculate the length when T=1.06s

g=9.8m/s² , π=3.124

$L=\frac{1.06^{2}*9.8 }{4*3.142^{2} }$

L=0.279m

the new period after its increased by  0.32s = 1.06+0.32 =1.38s

$L_{2}=\frac{1.38^{2}*9.8 }{4 *3.142^{2} }$

$L_{2}=0.473m$

increase in length = 0.473 -0.279

               =0.194m