A simple pendulum of length 1 m is oscillating with an angular frequency $10 \mathrm { rad } / \mathrm { s }$. The support of the pendulum starts oscillating up and down with a small angular frequency of $1 \mathrm { rad } / \mathrm { s }$ and an amplitude of $10 ^ { - 2 } \mathrm {~m}$. The relative change in the angular frequency of the pendulum is best given by:
(1) $10 ^ { - 3 } \mathrm { rad } / \mathrm { s }$
(2) $1 \mathrm { rad } / \mathrm { s }$
(3) $10 ^ { - 1 } \mathrm { rad } / \mathrm { s }$
(4) $10 ^ { - 5 } \mathrm { rad } / \mathrm { s }$