# 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

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

 1 $$\pi$$ 2 $$2 \pi$$ 3 $$4 \pi$$ 4 $$6 \pi$$
Subtopic:  Linear SHM |
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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
Subtopic:  Angular SHM |
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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) $\frac{1}{2}s$

(2) $\frac{1}{6}s$

(3) $\frac{1}{4}s$

(4) $\frac{1}{3}s$

Subtopic:  Simple Harmonic Motion |
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A second's pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket:

(1) Comes down with uniform acceleration

(2) Moves around the earth in a geostationary orbit

(3) Moves up with a uniform velocity

(4) Moves up with the uniform acceleration

Subtopic:  Simple Harmonic Motion |
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PMT - 1994
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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

Subtopic:  Angular SHM |
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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 on the moon where acceleration due to gravity is $\frac{1}{6}\mathrm{th}$ of the value of g on earth's surface?

 1 $$\frac{1}{\sqrt{6}} ~\mathrm{seconds}$$ 2 $$2 \sqrt{6}~ \mathrm{seconds}$$ 3 $$2~ \mathrm{seconds}$$ 4 $$12~\mathrm{ seconds}$$
Subtopic:  Spring mass system |
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A particle is executing SHM with an amplitude $$A$$ and the time period $$T$$. If at $$t=0$$, the particle is at its origin (mean position), then the time instant when it covers a distance equal to $$2.5A$$ will be:

 1 $$\dfrac{T}{12}$$ 2 $$\dfrac{5 T}{12}$$ 3 $$\dfrac{7 T}{12}$$ 4 $$\dfrac{2 T}{3}$$
Subtopic:  Linear SHM |
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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. $$\mu_s$$ 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 $$Q$$ will be:

1. $$kA$$
2. $$\frac{kA}{2}$$
3. zero
4. $$\mu_s mg$$

Subtopic:  Spring mass system |
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Which of the following figure represents damped harmonic motion?

 (i) (ii) (iii) (iv)

1. (i) and (ii)

2. (iii) and (iv)

3. (i), (ii), (iii), and (iv)

4. (i) and  (iv)

Subtopic:  Damped Oscillations (OLD NCERT) |
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