The uniform stick of mass m length L is pivoted at the centre. In the equilibrium position shown in the figure, the identical light springs have their natural length. If the stick is turned through a small angle θ, it executes SHM. The frequency of the motion is:

(1) 12π6Km

(2) 12π3K2m

(3) 12π3Km

(4) None of these

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If the displacement (x) and velocity v of a particle executing simple harmonic motion are related through the expression 4v2=25-x2 then its time period is:

(1) π

(2) 2π

(3) 4π

(4) 6π

Concept Questions :-

Simple harmonic motion
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Two simple pendulums have time periods T and 5T4. They start vibrating at the same instant from the mean position in the same phase. The phase difference between them when bigger pendulum completes one oscillation will be:

1. π6

2. π4

3. π3

4. π2

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Phasor diagram
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A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector a is correctly shown in 

(1)
(2)
(3)
(4)

Concept Questions :-

Simple harmonic motion
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A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude?

(1) 12s

(2) 16s

(3) 14s

(4) 13s

Concept Questions :-

Simple harmonic motion
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There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is T. If the resultant acceleration becomes g/4, then the new time period of the pendulum is 

(1) 0.8 T

(2) 0.25 T

(3) 2 T

(4) 4 T

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The time period of a spring mass system at the surface of earth is 2 second. What will be the time period of this system at mooon where  acceleration due to gravity is 16th of the value of earth's surface.

1.  16 seconds  

2.  26seconds 

3.  2 seconds 

4.  12 seconds

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A particle is executing SHM with amplitude A and time period T. If at t = 0, it is at origin mean position then find the time instant, whenit covers a distance equal to 5A2  

1.  T12  

2.  5T12  

3.  7T12  

4.  2T3

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A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure. μs is the coefficient of friction between P and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q is -

(1) kA

(2) kA2

(3) Zero

(4) μs mg

Concept Questions :-

Simple harmonic motion
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which of the following figure represents damped harmonic motion

1.  i and ii

2.  iii and iv

3.  i, ii, iii, and iv

4.  i, and  iv

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