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) $\frac{1}{2}s$

(2) $\frac{1}{6}s$

(3) $\frac{1}{4}s$

(4) $\frac{1}{3}s$

Concept Questions :-

Simple harmonic motion
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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 $\theta$, it executes SHM. The frequency of the motion is: (1) $\frac{1}{2\mathrm{\pi }}\sqrt{\frac{6K}{m}}$

(2) $\frac{1}{2\mathrm{\pi }}\sqrt{\frac{3K}{2m}}$

(3) $\frac{1}{2\mathrm{\pi }}\sqrt{\frac{3K}{m}}$

(4) None of these

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Angular SHM
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If the displacement (x) and velocity v of a particle executing simple harmonic motion are related through the expression $4{v}^{2}=25-{x}^{2}$ then its time period is:

(1) $\mathrm{\pi }$

(2) 2$\mathrm{\pi }$

(3) 4$\mathrm{\pi }$

(4) 6$\mathrm{\pi }$

Concept Questions :-

Simple harmonic motion
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Two simple pendulums have time periods T and $\frac{5T}{4}$. 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. $\frac{\mathrm{\pi }}{6}$

2. $\frac{\mathrm{\pi }}{4}$

3. $\frac{\mathrm{\pi }}{3}$

4. $\frac{\mathrm{\pi }}{2}$

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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 $\stackrel{\to }{a}$ is correctly shown in

 (1) (2) (3) (4) Concept Questions :-

Simple harmonic motion
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4.  $\frac{2\mathrm{T}}{3}$

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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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The displacement of a particle executing SHM is given by y = 0.25 (sin 200t) cm. The maximum speed of the particles is:

1.  200 cm/sec

2.  100 cm/sec

3.  50 cm/sec

4.  0.25 cm/sec

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