# Which one of the following is not an example of simple harmonic motion? 1. the motion of the Moon around the Earth as observed from Mars. 2. the ripples produced when a stone is dropped into a tank of water. 3. a weight moving up and down at the end of a spring. 4. the motion of a ball on the floor.

Subtopic:  Types of Motion |
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A mass is connected to a spring and it vibrates up and down, forming a simple harmonic system. Which of the following is/are correct?

 (a) The kinetic energy of the mass is at a maximum halfway up. (b) The potential energy of the system is at a maximum at the top of the mass's motion. (c) The potential energy of the system is at a maximum at the bottom of the mass's motion.

 1 a, b and c 2 a and b only 3 b only 4 c only
Subtopic:  Simple Harmonic Motion |
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The angular velocities of three bodies in simple harmonic motion are ${\omega }_{1},$ ${\omega }_{2},$ ${\omega }_{3}$ with their respective amplitudes as ${A}_{1},$ ${A}_{2},$ ${A}_{3}$. If all the three bodies have the same mass and maximum velocity, then:

 1 $$A_1 \omega_1=A_2 \omega_2=A_3 \omega_3$$ 2 $$A_1 \omega_1^2=A_2 \omega_2^2=A_3 \omega_3^2$$ 3 $$A_1^2 \omega_1=A_2^2 \omega_2=A_3^2 \omega_3$$ 4 $$A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2$$
Subtopic:  Simple Harmonic Motion |
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The total energy of a particle, executing simple harmonic motion is:

1. $\propto$ $x$

2. $\propto$ ${x}^{2}$

3.  Independent of x

4.  $\propto$ ${x}^{1/2}$

Subtopic:  Energy of SHM |
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A body is executing simple harmonic motion. At a displacement $$x$$, its potential energy is $$E_1$$ and at a displacement $$y$$, its potential energy is $$E_2$$${}_{}$. The potential energy $$E$$ at displacement $$x+y$$ will be?
1. $$E = \sqrt{E_1}+\sqrt{E_2}$$
2. $$\sqrt{E} = \sqrt{E_1}+\sqrt{E_2}$$
3. $$E =E_1 +E_2$$
4. None of the above

Subtopic:  Energy of SHM |
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The equation of motion of a particle is $${d^2y \over dt^2}+Ky=0$$ where $$K$$ is a positive constant. The time period of the motion is given by:

 1 $$2 \pi \over K$$ 2 $$2 \pi K$$ 3 $$2 \pi \over \sqrt{K}$$ 4 $$2 \pi \sqrt{K}$$
Subtopic:  Simple Harmonic Motion |
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The kinetic energy of a particle executing SHM is 16 J when it is in its mean position. If the amplitude of oscillations is 25 cm and the mass of the particle is 5.12 kg, the time period of its oscillation will be:
1. $\frac{\mathrm{\pi }}{5}sec$
2. $2\mathrm{\pi }$ $\mathrm{sec}$
3. $20\mathrm{\pi }$ $\mathrm{sec}$
4. $5\mathrm{\pi }$ $\mathrm{sec}$

Subtopic:  Energy of SHM |
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The period of oscillation of a simple pendulum of length $$\mathrm{L}$$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\theta$, is given by:

1.   $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{gcos\theta }}}$

2.  $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{gsin}\theta }}$

3.

4. $2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{gtan\theta }}}$

Subtopic:  Angular SHM |
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On a smooth inclined plane, a body of mass $$M$$ is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant $$K$$, the period of oscillation of the body (assuming the springs as massless) will be:

1. $$2\pi \left( \frac{M}{2K}\right)^{\frac{1}{2}}$$
2. $$2\pi \left( \frac{2M}{K}\right)^{\frac{1}{2}}$$
3. $$2\pi \left(\frac{Mgsin\theta}{2K}\right)$$
4. $$2\pi \left( \frac{2Mg}{K}\right)^{\frac{1}{2}}$$

Subtopic:  Combination of Springs |
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An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially un-stretched. Then the maximum extension in the spring will be:
1. 4 Mg/K
2. 2 Mg/K
3. Mg/K
4. Mg/2K

Subtopic:  Spring mass system |
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