chapter V

In a coupled system the extent to which one system influences the motion of the other is called --- of the system

• coupling

• coupling capacity

• limit of coupling

• oscillator

For undamped motion if the displacements are small then the restoring force due to mg will be ---

• $\frac{mg}{l}$

• $\frac{mgx}{l}$

• $\frac{x}{l}$

• $-k\left(x_2-x_1\right)$

The antisymmetric mode has ---- frequency than that of symmetric mode. 

• higher

• lower

• much smaller

• same

For symmetric mode of oscillations, the two pendulums oscillates with angular frequency ---

• $\sqrt{\frac{g}{l}}$

• $\sqrt{\frac{g}{l}+\frac{2k}{m}}$

• $\sqrt{\frac{g}{l}-\frac{2k}{m}}$

• $\sqrt{\frac{l}{g}}$

In coupled oscillations, the total potential energy V is expressed in terms of the normal coordinates as -----

• $\frac{mg}{4l}\left(X_1^2+X_2^2\right)+\frac{k}{2}X_2^2$

• $\frac{mg}{4l}\left(X_1^2-X_2^2\right)+\frac{k}{2}X_2^2$

• $\frac{m}{4}\left(X_1^2+X_2^2\right)+\frac{k}{2}X_2^2$

• $\frac{k}{2}\left(X_1^2-X_2^2\right)+\frac{mg}{4l}X_2^2$

The energy transfer from an oscillator to its coupled partner is periodic and takes place with the period

• $T=\frac{\pi}{\omega_1-\omega_2}$

• $T=\frac{2\pi}{\omega_1-\omega_2}$

• $T=\frac{4\pi}{\omega_1-\omega_2}$

• $T=\frac{\pi}{4\left(\omega_1-\omega_2\right)}$

If the amplitude of oscillations remains the same the same then the motion is called ----

• undamped

• damped

• over damped

• critically damped

If the amplitude of oscillations remain the same then that type of oscillations are called

• damped oscillations

• undamped oscillations

• over damped oscillations

• critically damped oscillations

In case of coupled system of two simple pendulums ----

• the frequency of symmetric mode is equal to frequency of antisymmetric mode

• frequency of symmetric mode is greater than that of antisymmetric mode

• frequency of symmetric mode is less than that of antisymmetric mode

• frequencies are multiple of each other

In antisymmetric mode of oscillations, the particles are oscillating always -----

• out of phase

• in phase

• with phase difference of 45⁰

• with phase difference of 90⁰