Question 105: Oscillations

Question

A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of 10
–2
m. The relative change in the angular frequency of the pendulum is best given by :

Accepted Answer

Angular frequency of pendulum
$$\omega $$ = $$\sqrt {{{{g_{eff}}} \over \ell }} $$
$$ 	herefore $$   $${{\Delta \omega } \over \omega }$$ = $${1 \over 2}$$ $${{\Delta {g_{eff}}} \over {{g_{eff}}}}$$
$$\Delta $$$$\omega $$ = $${1 \over 2}$$ $${{\Delta g} \over g} 	imes \omega $$
[$${\omega _s}$$ = angular frequency of support]
$$\Delta $$$$\omega $$ = $${1 \over 2} 	imes {{2A\omega _s^2} \over {100}} 	imes 100$$
$$\Delta \omega  = {10^{ - 3}}$$ rad/sec.

Answer

1 rad/s

Answer

10
$$-$$3
rad/s

Answer

10
$$-$$1
rad/s

Answer

10
$$-$$5
rad/s

Oscillations

A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of 10 –2 m. The relative change in the angular frequency of the pendulum is best given by :

Choose the correct answer: