Damped Oscillations

Q.

The kinetic energy of a particle executing S.H.M. is 16 J when it is in its mean position. If the amplitude of oscillations is 25 cm and the mass of the particle is 5.12 kg, the time period of its oscillation is

[Haryana CEE 1996; AFMC 1998]

1. 

2. 

3. 

4. 

Q.

The string of pendulum of length I is displaced through ${90}^{\circ }$ from the vertical and released. Then the minimum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is

1. 

2. 

3. 

4. 

Q. a vibration magnetometer placed in magnetic meridian has a small bar magnet .the magnet executes oscillations with a time period of 2s in earths horizontal magnetic field of 24 microtesla when a horizontal field of 18 micro tesla is produced opposite to the earths field by placing a current carrying wire the new time period will be

Q.

Beats are produced by the superposition of two harmonic waves if:

1. a) their amplitudes and frequencies are equal

2. b) their amplitudes are the same but their frequencies differ slightly

3. c) their frequencies differ slightly even if their amplitudes are not equal

4. d) both (b) and (c)

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.

For the damped oscillator system shown with m = 250g, k = 85 N/m, and b = 70 g/s, what is the ratio of the oscillation amplitude at the end of 20 cycles to the initial oscillation amplitude?

1. 1:2

2. 20:21

3. 19:50

4. 5:6

Q. You are riding in an automobile of mass 3000 kg. Assuming that you are examiningthe oscillation characteristics of its suspension system. The suspension sags15 cm when the entire automobile is placed on it. Also, the amplitude of oscillationdecreases by 50% during one complete oscillation. Estimate the values of (a) thespring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports 750 kg.

Q.

What is the first natural frequency?

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. 13.A lightly damped oscillatorwith frequency v is set is motion by a harmonic driving force of frequency v .When v < v, then response of the osscilator is cntrolled by a oscillator frequency b spring constant c inertia of the mass d damping coefficient

Q.

In a stationary wave, all particles are

[MP PMT 1994]

1. At rest at the same time twice in every period of oscillation

2. Never at rest at the same time

3. At rest at the same time only once in every period of oscillation

4. Never at rest at all

Q.

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half-submerged in a liquid of density $\rho$ at equilibrium position. When the cylinder is given a small downward push and released it starts oscillating vertically with a small amplitude. If the force constant of the spring is k, the frequency of oscillation of the cylinder is :

1. 

2. $\frac{1}{2\pi }(\frac{k+A\rho g}{M}{)}^{\frac{1}{2}}$

3. $\frac{1}{2\pi }(\frac{k+\rho g{L}^2}{M}{)}^{\frac{1}{2}}$

4. $\frac{1}{2\pi }(\frac{k+A\rho g}{Apg}{)}^{\frac{1}{2}}$

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. 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. How torsional pendulum works? Difference between torsional pendulum and simple pendulum?

Q. In damped oscillations, if the amplitude becomes half of its maximum value in $1\text{s}$, then after $2\text{s}$ amplitude will be
($A_o$ is initial amplitude)

1. $\frac{A_o}{4}$
2. $\frac{A_o}{2}$
3. $A_o$
4. $\frac{\sqrt{3}{A}_o}{2}$

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. A metalic ring connected to a rod oscillates freely like a pendulum. If now a magnetic field is applied in horizontal diection so that the pendulum now swings through the field, the pendulum will come to rest very soon.(i)What if it was not a complete ring or rather a semicircular part of the ring, then what would have been the case?(ii)How to make it continue its oscillatory motion?

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 wire loop is rotated in a magnetic field.The frequency of change of direction of the induced e.m.f.is (1) Twice per revolution (2) Four times per revolution (3) Six times per revolution (4) Once per revolution