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.

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

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

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)

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

For damped oscillations, the graph between energy and time will be:

1.		2.
3.		4.

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

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

The amplitude of an S.H.M. reduces to \(1/3\) in first \(20\) s, then in first \(40\) s its amplitude becomes:
1. \(1\over 3\)
2. \(1\over 9\)
3. \(1\over 27\)
4. \(\frac{1}{\sqrt{3}}\)