The amplitude of velocity of a particle is given by, ${\mathrm{V}}_{\mathrm{m}}={\mathrm{V}}_0/\left({\mathrm{a\omega }}^2-\mathrm{b\omega }+\mathrm{c}\right)$ where ${\mathrm{V}}_0,\mathrm{a},\mathrm{b},\mathrm{c}$ are positive:

The condition for a single resonant frequency is 

1. ${\mathrm{b}}^2<4\mathrm{ac}$

2. ${\mathrm{b}}^2=4\mathrm{ac}$

3. ${\mathrm{b}}^2=5\mathrm{ac}$

4. ${\mathrm{b}}^2=7\mathrm{ac}$

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

In the following questions, a statement of assertion (A) is followed by a statement of the reason (R).

1.  If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).

2.  If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).

3.  If Assertion is a true statement but Reason is false, then mark (3).

4.  if both Assertion and Reason are false statements, then mark (4).

A: The periodic time of a hard spring is more as compared to the soft spring.

R: The spring constant of hard spring is less.