Gamma Question Bank for Engineering Physics>Chapter 13 - Oscillations>Assignment>Q 11

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Consider the shown arrangement. Rod is massless which can rotate freely about hinge $O .$ All the springs are ideal and massless. If frequency of small oscillations of block $m$ (Neglect gravity) is $f = \frac{1}{2 π} \sqrt{\frac{N k}{9 m}}$ , then find value of $N .$

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Important Questions on Oscillations

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Gamma Question Bank for Engineering Physics>Chapter 13 - Oscillations>EXERCISE 13.1>Q 1

Two particles are in SHM in parallel straight lines close to each other. Amplitude

A

and time period

T

of both the particles are equal. At time

t = 0

, one particle is at displacement

y_{1} = + A

and other at

y_{2} = - \frac{A}{2}

, and they are approaching toward each other. After what time they will cross each other?

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Gamma Question Bank for Engineering Physics>Chapter 13 - Oscillations>EXERCISE 13.1>Q 2

The time taken by a particle performing SHM on a straight line to pass from point

A

to

B

, where its velocities are same, is

2

seconds. After another

2

seconds it returns to

B

. The time period of oscillation is (in seconds):

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Gamma Question Bank for Engineering Physics>Chapter 13 - Oscillations>EXERCISE 13.1>Q 3

Time period of a particle executing SHM is

8

second. At

t = 0

it is at the mean position. The ratio of distance covered by the particle in the

1^{st}

second to the

2^{nd}

second

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Gamma Question Bank for Engineering Physics>Chapter 13 - Oscillations>EXERCISE 13.1>Q 5

Two simple harmonic motions are represented by

y_{1} = 5 [\sin 2 π t + \sqrt{3} \cos 2 π t], y_{2} = 5 \sin (2 π t + \frac{π}{4})

The ratio of their amplitudes is

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Gamma Question Bank for Engineering Physics>Chapter 13 - Oscillations>EXERCISE 13.2>Q 6

When the maximum

K E

of a simple pendulum is

K

, then what is its displacement (in terms of amplitude a), when its

K E

is

\frac{K}{2} ?

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Gamma Question Bank for Engineering Physics>Chapter 13 - Oscillations>EXERCISE 13.2>Q 7

The kinetic energy of a simple harmonic motion when the particle is half way to its end point is (where

E_{0}

is the total energy)

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Gamma Question Bank for Engineering Physics>Chapter 13 - Oscillations>EXERCISE 13.2>Q 8

For a particle executing simple harmonic motion, the kinetic energy

K

is given by,

K = K_{0} \cos^{2} ω t .

The maximum value of potential energy is

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Gamma Question Bank for Engineering Physics>Chapter 13 - Oscillations>EXERCISE 13.2>Q 9

Starting from the origin, a body oscillates simple harmonically with a period of

2 s

. After what time will its kinetic energy be

75 %

of the total energy?