A particle with restoring force proportional to the displacement and resisting force proportional to velocity is subjected to a force, $\mathrm{F}={\mathrm{F}}_{0<mspace\; width="1em"></mspace>}\sin <mspace\; width="1em"></mspace>\mathrm{\omega t}$

If, the amplitude of the particle is maximum for $\mathrm{\omega }={\mathrm{\omega }}_1$ and the energy of the particle is maximum for $\mathrm{\omega }={\mathrm{\omega }}_2$, then

1. ${\mathrm{\omega }}_1={\mathrm{\omega }}_0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{\omega }}_2\ne {\mathrm{\omega }}_0$

2. ${\mathrm{\omega }}_1={\mathrm{\omega }}_0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{\omega }}_2={\mathrm{\omega }}_0$

3. ${\mathrm{\omega }}_1\ne {\mathrm{\omega }}_0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{\omega }}_2={\mathrm{\omega }}_0$

4. ${\mathrm{\omega }}_1\ne {\mathrm{\omega }}_0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{\omega }}_2\ne {\mathrm{\omega }}_0$

In a forced oscillation, when the system oscillates under the action of the driving force $\mathrm{F}$ $=$ ${\mathrm{F}}_0$ $\sin$ $\mathrm{\omega t}$ in addition to its internal restoring force, the particle oscillates with a frequency equal to

1.  The natural frequency of the body

2.  Frequency of driving force

3.  The difference in frequency of driving force and natural frequency

4.  Mean of the driving frequency and natural frequency

For forced oscillations, a particle oscillates in a simple harmonic fashion with a frequency equal to:

1. the frequency of driving force.

2. the mean of frequency of driving force and natural frequency of the body.

3. the difference of frequency of driving force and natural frequency of the body.

4. the natural frequency of the body.

In case of a forced vibration, the resonance wave becomes very sharp when the:
1. Damping force is small
2. Restoring force is small
3. Applied periodic force is small
4. Quality factor is small

The figure given below shows the graphs for amplitudes of forced oscillations in resonance conditions for different damping conditions. 

One of the conclusions that can be drawn from the graph above is:

1. As damping increases, amplitude increases

2. As damping increases, the amplitude decreases

3. As damping increases, the amplitude does not change

4. As damping increases, the amplitude may increase or decrease