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A charged ball of positive charge $q_{1}$ is revolving around another positive charge $q$ as shown in a conical pendulum. The motion is in a horizontal plane :-

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Important Questions on Simple Harmonic Motion

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

Two identical charged spheres suspended from a common point by two massless strings of lengths

l

, are initially at a distance

d (d ≪ l)

apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity

υ

. Then

υ

varies as a function of the distance

x

between the spheres, as

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

In case of a forced vibration, the resonance wave becomes very sharp when the:

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

In a parallel LCR circuit, the current at resonance will be

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

The dimensional formula of coefficient of permittivity for free space (

ε_{0}

) in the equation

F = \frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{r^{2}},

where symbols have their usual meanings, is

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

A simple harmonic oscillator of angular frequency

2 rad s^{- 1}

is acted upon by an external force

F = \sin t N .

If the oscillator is at rest in its equilibrium position at

t = 0,

its position at later times is proportional to:

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

Two charges, each equal to

q

, are kept at

x = - a

and

x = a

on the x-axis. A particle of mass

m

and charge

q_{0} = - \frac{q}{2}

is placed at the origin. If charge

q_{0}

is given a small displacement

(y ≪ a)

along the y-axis, the net force acting on the particle is proportional to :

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

What do you understand by free vibrations of a body?

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

Two charges of equal magnitudes and at a distance $r$ exert a force $F$ on each other. If the charges are halved and distance between them is doubled, then the new force acting on each charge is

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

A stretched wire vibrates with a frequency of

60 Hz

when the tension in the wire is

T_{1}

and with a frequency of

130 Hz

when the tension in the wire is

T_{2}

. If the tension in the wire is

(T_{1} + T_{2}),

its frequency of vibration is

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

Consider a driven damped mechanical oscillator is in resonance. Which of the following statements is true ?

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

Two identical conducting spheres

A

and

B

carry an equal charges. They are separated by a distance much larger than their diameters, and the force between them is

F

. A third identical conducting sphere,

C

, is uncharged. Sphere

C

is first touched to

A

, then to

B

, and then removed. As a result, the force between

A

and

B

would be equal to:

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

Define resonant vibrations.

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

Suppose the charge of a proton and an electron differ slightly. One of them is

e

, the other is

(e + Δ e)

. If the net electrostatic force and gravitational force between two hydrogen atoms placed at a distance

d

(much greater than atomic size) apart is zero, then

Δ e

is of the order of [Given mass of hydrogen

m_{h} = 1.67 \times 10^{- 27} kg

]

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

A length - scale

(l)

depends on the permittivity

(ε)

of a dielectric material, Boltzmann constant

k_{B}

, the absolute temperature T, the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles, Which of the following expressions (s) for

l

is (are) dimensionally correct?

MEDIUM

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

Three concentric metal shells

A, B

and

C

of respective radii

a, b

and

c (a < b < c)

have surface charge densities

+ σ, - σ

and

+ σ

respectively. The potential of shell

B

is:

HARD

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

A certain charge

2 Q

is divided at first into two parts

q_{1}

and

q_{2}

. Later the charges are placed at a certain distance. If the force of interaction between two charges is maximum then

\frac{Q}{q_{1}} =

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

Two point charges A and B, having charges

+ Q

and

- Q

respectively, are placed at certain distance apart and force acting between them is

F

. If

25 %

charge of

A

is transferred to

B

, then the force between the charges becomes

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

The phenomenon that occurs when the frequency of forced vibrations on an object matches the natural frequency of that object, and produces a dramatic increase in amplitude is called

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

In Melde's experiment, when the tension decreases by

0.009 kg - wt

, the number of loops changes from

4

5

. The initial tension is

EASY

Physics>Oscillations and Waves>Simple Harmonic Motion>Forced Oscillations

Two pendulums $C$ and $D$ are suspended from a wire as shown in the given figure. Pendulum $C$ is made to oscillate by displacing it from its mean position. It is seen that $D$ also starts oscillating. Name the type of oscillation, $D$ will execute.

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A charged ball of positive charge q1 is revolving around another positive charge q as shown in a conical pendulum. The motion is in a horizontal plane :-

Important Questions on Simple Harmonic Motion

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A charged ball of positive charge $q_{1}$ is revolving around another positive charge $q$ as shown in a conical pendulum. The motion is in a horizontal plane :-