Damped Oscillations

Q. A spring is stretched by $5\text{cm}$ by a force $10\text{N}$. The time period of the oscillations when a mass of $2\text{kg}$ is suspended by it is

1. $0.628\text{s}$
2. $0.314\text{s}$
3. $3.14\text{s}$
4. $0.314\text{s}$

Q. A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is -

1. 254 Hz
2. 246 Hz
3. 240 Hz
4. 260 Hz

Q. In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value $a_0$ at the end of $100$ oscillations. When the oscillator completes $200$ oscillations, its amplitude must be

1. $\frac{a_0}{2}$
2. $\frac{a_0}{4}$
3. $\frac{a_0}{6}$
4. $\frac{a_0}{9}$

Q.

Calculate the dimensions of force and impulse taking velocity, density and frequency as the basic quantities

Q. The amplitude of a damped oscillator becomes one-fourth in one minute. The amplitude after 16 minutes will be ${\frac{1}{x}}^{th}$ of its original amplitude. Find the value of $x.$

1. $2^4$
2. $2$
3. $2^{16}$
4. $2^{32}$

Q.

When two tuning forks A and B are sounded together, 4 beats per second are heard. The frequency of the fork B is 384 Hz. When one of the prongs of the fork A is filed and sounded with B, the beat frequency increases, then the frequency of the fork A is

1. 379 Hz

2. 380 Hz

3. 389 Hz

4. 388 Hz

Q.

Does damping affect natural frequency?

Q. Which of the following figures represents damped harmonic motion?

1. 
2. 
3. 
4. 

Q.

For the damped oscillator shown, the mass m of the block is 200 g, k = 90 N m${}^{-1}$ and the damping constant b is 40 g s${}^{-1}$. What is the period of oscillation, time taken for its amplitude of vibrations to drop to half of its initial value.

1. 1s, 6.93s

2. 0.3s, 6.93s

3. 0.6s, 6.93s

4. 0.3s, 3s

Q. A particle of mass $10gm$ is placed in a potential field given by $V=(50x^2+100)J/kg$. The frequency of ascillation in $cycle/sec$ is :

1. $\frac{50}{\pi }$
2. $\frac{100}{\pi }$
3. $\frac{10}{\pi }$
4. $\frac{5}{\pi }$

Q. Two springs of force constants $k_1$ and $k_2$ are connected as shown figure. The time period of vertical oscillations of mass m is given by

1. 
2. 
3. 
4. 

Q. The length of a magnet is very large as compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2 s. The magnetic is cut perpendicular to its length in to three equal parts and three parts are then placed on each other with their like poles together. The time period of this combination will be (1) 2 s(2) 2/3 s (3)2\sqrt3s (4)2/\sqrt[{}]3

Q. The amplitude of a damped oscillation becomes half in $1\text{minute}$. If the amplitude after $4\text{minute}$ will be $\frac{1}{y}$ times of the original, find the value of $y$.

1. $4$
2. $8$
3. $16$
4. $32$

Q. 34.a conducting ring of radius 1 meter is placed in an uniform magnetic field B of 0.01 tesla oscillation with frequency 100 hz with its plane at right angle to B.What will be the induced electric field?

Q. In damped oscillations, damping force is directly proportional to the speed of the oscillator. If amplitude becomes half of its initial value in $1\text{s}$, then after $2\text{s}$, amplitude will be:
[$A_0$ is initial amplitude]

1. $\frac{1}{4}{A}_0$
2. $\frac{1}{2}{A}_0$
3. $A_0$
4. $\frac{\sqrt{3}{A}_0}{2}$

Q. In case of damped oscillation the frequency of oscillation is

1. greater than natural frequency
2. less than natural frequency
3. equal to natural frequency
4. both $\left(a\right)$ and $\left(b\right)$

Q. A particle is acted simultaneously by mutually perpendicular simple harmonic motion $x=a\cos \omega t$ and $y=a\sin \omega t$. The trajectory of motion of the particle will be

1. a parabola
2. a straight line
3. an ellipse
4. a circle

Q. A tuning fork of frequency 480 Hz produces 10 beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces lesser beats per second than before

1. 460 Hz
2. 470 Hz
3. 480 Hz
4. 490 Hz

Q.

What does the poet like to do when it rains?

Q. The total energy of a particle executing S.H.M. is proportional to

1. Velocity in equilibrium position
2. Displacement from equilibrium position
3. Frequency of oscillation
4. Square of amplitude of motion

Q.

What is the basic principle of Oscillation?

Q.

The figure shows velocity ($v)$ versus time ($t$) graph for two cyclist moving along the same straight segment of a highway from the same point. the second cyclist starts moving at $t=3\text{min}$ At what time (in minute) do the two cyclists meet?

Q. In the case of sustained forced oscillations the amplitude of oscillations,

1. Decreases sinusoidally
2. Decreases exponentially
3. Always remains constant
4. Decreases linearly

Q. A weakly damped harmonic oscillator of frequency $n_1$ is driven by an external periodic force of frequency $n_2$. When the steady state is reached, the frequency of the oscillator will be

1. $n_1$
2. $n_2$
3. $\frac{n_1+n_2}{2}$
4. $(n_1+n_2)$

Q. A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length 20 cm, fixed at its mid point. The bob is displaced slightly, perpendicular to the plane of the rod and string. The period of small oscillations of the system is found to be $\frac{\pi X}{10}sec.$, then find the value of $X$. ($g=10m/s^2)$ (Answer upto two digit after decimal places)

Q.

Answer the following: When you switch off the fan, it soon comes to rest. Why?

Q. A mass of $50\text{kg}$ is suspended from a spring of stiffness $10\text{kN/m}$. It is set into oscillations and it is observed that two successive oscillations have amplitudes $10\text{mm}$ and $1\text{mm}$. Determine the damping ratio.

1. $0.232$
2. $0.344$
3. $0.392$
4. $0.446$

Q. The Bob of a simple pendulum is replaced by a magnet. The oscillation are set along the length of the magnet. A copper coil is added so that one pole of the magnet passes in and out of the coil. The coil is shortcircuted. Then which of the following happens? 1) period does not change 2) Oscillations are damped 3) amplitude increases 4) period decreases

Q.

Vibrations, whose amplitude of oscillation decreases with time are called

1. free vibrations

2. forced vibrations

3. damped vibrations

4. none of these

Q. Water is filled in $\text{U}$ shaped tube up to height $H$ on both sides. If we displace a liquid column of any one side by $x\text{cm}$. What is the time period of oscillation of liquid column ?
Mass of water per unit length $=50\text{g}$.

1. $3.2\text{s}$
2. $2.8\text{s}$
3. $2.0\text{s}$
4. $1.4\text{s}$