A 20 g particle is subjected to two simple harmonic motions x 1 = 2 sin 10 t , x 2 = 4 sin 10 t + π 3 , where x 1 and x 2 are in metre and t is in second. Choose the correct option(s).

Energy of the resultant motion will be 28 J .

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The potential energy $U$ of a body of unit mass moving in one dimensional conservative force field is given by $U = x^{2} - 4 x + 3 .$ All units are in SI. For this situation mark out the correct statement(s).

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Important Questions on Linear and Angular Simple Harmonic Motion

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 5 - Linear and Angular Simple Harmonic Motion>Exercises>Q 11

A particle performing simple harmonic motion undergoes initial displacement of

A / 2

(where

A

is the amplitude of simple harmonic motion) in

1 s .

t = 0,

the particle may be at the extreme position or mean position. The time period of the simple harmonic motion can be

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 5 - Linear and Angular Simple Harmonic Motion>Exercises>Q 12

A particle is subjected to two simple harmonic motions along x and y directions according to, x = 3 sin 100 πt; Y = 4 sin 100πt.

HARD

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 5 - Linear and Angular Simple Harmonic Motion>Exercises>Q 13

The speed

v

of a particle moving along a straight line, when it is at a distance (

x

) from a fixed point of the line is given by

v^{2} = 108 - 9 x^{2}

(all quantities are in CGS units). Which of the following is/are true?

HARD

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 5 - Linear and Angular Simple Harmonic Motion>Exercises>Q 14

A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of 40 cm. The block just loses contact with the plank when the latter is at momentary rest. Then–

HARD

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 5 - Linear and Angular Simple Harmonic Motion>Exercises>Q 15

20 g

particle is subjected to two simple harmonic motions

x_{1} = 2 \sin 10 t

x_{2} = 4 \sin (10 t + \frac{π}{3})

, where

x_{1}

and

x_{2}

are in metre and

t

is in second. Choose the correct option(s).

EASY

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 5 - Linear and Angular Simple Harmonic Motion>Exercises>Q 17

The time period of a particle in simple harmonic motion is

T .

Assume potential energy at mean position to be zero. After a time of

\frac{T}{6}

it passes its mean position, its

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 5 - Linear and Angular Simple Harmonic Motion>Exercises>Q 18

An object of mass $m$ is performing simple harmonic motion on a smooth horizontal surface as shown in the figure. Just as the oscillating object reaches its extreme position, another object of mass $2 m$ is dropped on to oscillating object, which sticks to it. For this situation mark out the correct statement(s).

Question Image

HARD

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 5 - Linear and Angular Simple Harmonic Motion>Exercises>Q 19

The given Fig. (a) shows a spring of force constant $k$ fixed at one end and carrying a mass $m$ at the other end placed on a horizontal frictionless surface. The spring is stretched by a force $F .$ Figure (b) shows the same spring with both ends free and a mass $m$ fixed at each free end. Each of the spring is stretched by the same force $F .$ The mass in case (a) and the masses in case (b) are then released. Which of the following statements are true?

Question Image

The potential energy U of a body of unit mass moving in one dimensional conservative force field is given by U=x2-4x+3. All units are in SI. For this situation mark out the correct statement(s).

Important Questions on Linear and Angular Simple Harmonic Motion

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The potential energy $U$ of a body of unit mass moving in one dimensional conservative force field is given by $U = x^{2} - 4 x + 3 .$ All units are in SI. For this situation mark out the correct statement(s).