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What is the frequency with which forced periodic oscillations oscillate?

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Important Questions on Simple Harmonic Motion

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

A damped harmonic oscillator has a frequency of

5

oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to

\frac{1}{1000}

of the original amplitude is close to:

HARD

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

A pendulum with the time period of $1 s$ is losing energy due to damping. At a certain time, its energy is $45 J$ . If after completing $15$ oscillations its energy has become $15 J$ , then its damping constant (in $s^{- 1}$ ) will be

EASY

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

The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693).

HARD

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

A rectangular block of mass

m

and area of cross-section

A

floats in a liquid of density

ρ

. If it is given a vertical displacement from equilibrium, it undergoes oscillation with a time period

T

. Then

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

The displacement of a damped harmonic oscillator is given by

x (t) = e^{- 0.1 t} \cos (10 π t + φ) .

Here

t

is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to:

EASY

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

A block of mass

0.1 kg

is connected to an elastic spring of spring constant

640 N m^{- 1}

and oscillates in a damping medium of damping constant

10^{- 2} kg s^{- 1}

. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to-

EASY

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

The amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass

= 500 g

, Decay constant

= 20 g s^{- 1}

then how much time is required for the amplitude of the system to drop to half of its initial value?

(\ln 2 = 0.693)

EASY

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

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

HARD

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

A cylindrical plastic bottle of negligible mass is filled with

310 ml

of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency

ω .

If the radius of the bottle is

2 .5 cm

then

ω

is close to:

(

density of water

= 10^{3} kg m^{- 3})

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

A cylindrical block of wood of mass

10 kg

and radius

10 cm

is floating in water with its axis vertical. When it is depressed a little and then released, it starts executing simple hormonic motion (SHM). The frequency of the SHM, executed by the block is:
(Assume

g = 10 m s^{- 2}

and let

ρ

is the density of the water)

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.

Question Image

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

The amplitude of a damped oscillator becomes half in one minute. The amplitude after

3

minutes will be

\frac{1}{x}

times the original. Then

x

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

A simple pendulum oscillating in air has period

T

. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is

\frac{1}{16} t h

of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:

EASY

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

A block of mass

1 kg

attached to a spring is made to oscillate with an initial amplitude of

12 cm

. After

2

minutes the amplitude decreases to

6 cm

. Determine the value of the damping constant for this motion. (take

\ln 2 = 0.693

)

EASY

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

The system that returns to equilibrium as quickly as possible without oscillating is

EASY

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

Instantaneous power delivered to a damped harmonic oscillator (natural frequency is

ω_{0}),

by an external periodic force (driving frequency

ω)

under steady state conditions is

MEDIUM

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

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to

α

times its original magnitude, where

α

equals :

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 ?

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:

What is the frequency with which forced periodic oscillations oscillate?

Important Questions on Simple Harmonic Motion

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