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Which one of the following equations of motion represents a simple harmonic motion ?

(A)

Acceleration =-k_{0} x + k_{1} x^{2}

(B)

Acceleration = -k(x+a)

(C)

Acceleration = k(x+a)

(D)

Acceleration - kx where k,k_{0},k_{1} and a are all positive

Question-2

A particle executes simple harmonic motion of amplitude A. At what distance from the mean position its kinetic energy is equal to its potential energy ?

(A)

0.51 A

(B)

0.61 A

(C)

0.71 A

(D)

0.81 A

Question-3

A particle is subjected to two mutually perpendicular simple harmonic motions such that is x and y coordinates are given by

The path of the particle will be:

(A)

A straight line

(B)

A circle

(C)

An ellipse

(D)

A parabola

Question-4

A simple pendulum performs simple harmonic motion about x=0 with an amplitude a and time period T. The speed of the pendulum at will be:

(A)

(B)

(C)

(D)

Question-5

A body is vibrating in S.H.M. with an amplitude of 0.06 m and frequency of 15 Hz. The maximum velocity and acceleration of the body are:

(A)

5.65 m/s, 5.32 x 10^{2} m/s^{2}

(B)

6.82 m/s, 7.62 x 10^{2} m/s^{2}

(C)

8.91 m/s, 8.21 x 10^{2} m/s^{2}

(D)

9.82 m/s, 9.03 x 10^{2} m/s^{2}

Question-6

The frequency of a simple pendulum in a freely falling lift will be :

(A)

Zero

(B)

Infinite

(C)

Finite

(D)

Cannot say

Question-7

A linear harmonic oscillator of force constant 2 x 10^{6} N/m and amplitude 0.01 m has a total mechanical energy of 160 J. Which of the following statement is true ?

(A)

Maximum potential energy is 160 J

(B)

Maximum potential energy is 100 J

(C)

Maximum potential energy is zero

(D)

Minimum potential energy is 100 J

Question-8

A particle moving along the X-axis executes simple harmonic motion; then the force acting on it is given by:

(A)

-AKx

(B)

A cos Kx

(C)

A exp(-Kx)

(D)

AKx

Question-9

Two springs of spring constants k_{1}and k_{2} are joined in series. The effective spring constant of the combination is given by:

(A)

(B)

(C)

k_{1} + k_{2}

(D)

Question-10

A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force F sin. If the amplitude of the particle is maximum for =_{1}, and the energy of the particle is maximum for = _{2}, then:

(A)

_{1} = _{0} and _{2}_{0}

(B)

_{1} = _{0} and _{2} = _{0}

(C)

_{1}_{0} and _{2} = _{0}

(D)

_{1}_{0} and_{2}_{0}

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