Which of the following figure represents damped harmonic motion?

(i)
(ii)
(iii)
(iv)

1. (i) and (ii)

2. (iii) and (iv)

3. (i), (ii), (iii), and (iv)

4. (i) and  (iv)

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are 

1.$\mathrm{ k}g m{s}^{-1}$                               

2.$\mathrm{ k}g m{s}^{-2}$

3. $kg s^{-1}$                                   

4. $kg s$

 Amplitude of a wave is represented by

$A=\frac{c}{a+b-c}$

Then resonance will occur when

1.     $b=-c/2$              

2.     b = 0 and a =  c

3.     $b=-a/2$              

4.     None of these

Which of the following figure represent(s) damped simple harmonic motions?

1. 

2. 

3. 

4. 

The amplitude of the damped oscillator becomes (1/3) in 2s. Its amplitude after 6s is 1/n times the original. Then n is equal to:

1. $2^3$

2. $3^2$

3. $3^{1/3}$

4. $3^3$

The amplitude of a simple harmonic oscillator is A and speed at the mean position is ${\mathrm{v}}_0$. The speed of the oscillator at the position $\mathrm{x} = \frac{\mathrm{A}}{\sqrt{3}}$ is:

1.  $\frac{2v_0}{\sqrt{3}}$

2.  $\frac{\sqrt{2}{v}_0}{3}$

3.  $\frac{2}{3}{v}_0$

4.  $\frac{\sqrt{2}{v}_0}{\sqrt{3}}$

The amplitude of a damped oscillator becomes one-third in 10 minutes and $\frac{1}{\mathrm{n}}$ times of the original value in 30 minutes. The value of n is:

1.  81

2.  3

3.  9

4.  27

A particle executes simple harmonic oscillations under the effect of small damping. If the amplitude of oscillation becomes half of the initial value of 16 mm in five minutes, then what will be the amplitude after fifteen minutes?

1.  8 mm

2.  4 mm

3.  2 mm

4.  1 mm

A body executes oscillations under the effect of a small damping force. If the amplitude of the body reduces by 50% in 6 minutes, then amplitude after the next 12 minutes will be [initial amplitude is ${\mathrm{A}}_0$] -

1.  $\frac{{\mathrm{A}}_0}{4}$

2.  $\frac{{\mathrm{A}}_0}{8}$

3.  $\frac{{\mathrm{A}}_0}{16}$

4.  $\frac{{\mathrm{A}}_0}{6}$

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.