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A system of two identical rods ( $L$ -shaped) of mass $m$ and length $l$ are resting on a peg $P$ as shown in the figure. It the system is displaced in its plane by a small angle $θ$ , find the period of oscillations

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Important Questions on Simple Harmonic Motion

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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 27

The distance of point of a compound pendulum from its centre of gravity is

l

, the time period of oscillation relative to this point is

T

. If

g = π^{2}

, the relation between

l

and

T

will be,

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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 28

A man of mass

60 kg

standing on a plateform executing S.H.M. in the vertical plane. The displacement from the mean position varies as

y = 0.5 \sin (2 π ft)

. The minimum value of

f

, for which the man will feel weightlessness at the highest point is: (

y

is in metres)

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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 29

A heavy brass-sphere is hung from a spring and it executes vertical vibrations with period

T

. The ball is now immersed in nonviscous liquid with a density one-tenth that of brass. When set into vertical vibrations with the sphere remaining inside the liquid all the time, the period will be:

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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 30

A particle of mass

m

moves in a one-dimensional potential energy

U (x) = - a x^{2} + b x^{4}

, where

a

and

b

are positive constants. The angular frequency of small oscillations about the minima of the potential energy is equal to

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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 31

A particle performs SHM of amplitude

A

along a straight line. When it is at a distance

\frac{\sqrt{3}}{2} A

from the mean position, its kinetic energy gets increased by an amount

\frac{1}{2} m ω^{2} A^{2}

due to an impulsive force. Then its new amplitude becomes:

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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 32

A particle executes SHM on a line

8 cm

long. Its

K . E .

and

P . E .

will be equal when its distance from the mean position is:

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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 33

The total energy of a vibrating particle in S.H.M. is $E$ . If its amplitude and time period are doubled, its total energy will be:

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Beta Question Bank for Engineering: Physics>Chapter 19 - Simple Harmonic Motion>Exercise-1>Q 34

The distance between the point of suspension and the centre of gravity of a compound pendulum is

l

and the radius of gyration about the horizontal axis through the centre of gravity is

k

. Then, its time period will be,

A system of two identical rods (L-shaped) of mass m and length l are resting on a peg P as shown in the figure. It the system is displaced in its plane by a small angle θ, find the period of oscillations

Important Questions on Simple Harmonic Motion

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A system of two identical rods ( $L$ -shaped) of mass $m$ and length $l$ are resting on a peg $P$ as shown in the figure. It the system is displaced in its plane by a small angle $θ$ , find the period of oscillations