# A particle is executing linear simple harmonic motion with an amplitude $$a$$ and an angular frequency $$\omega$$. Its average speed for its motion from extreme to mean position will be: 1. $$\frac{a\omega}{4}$$ 2. $$\frac{a\omega}{2\pi}$$ 3. $$\frac{2a\omega}{\pi}$$ 4. $$\frac{a\omega}{\sqrt{3}\pi}$$

Subtopic:  Linear SHM |
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Two simple harmonic motions, $$y_1 = a \sin\omega t$$ and $$y_2 = 2a\sin\left(\omega t+\frac{2\pi}{3}\right)$$ are superimposed on a particle of mass $$m$$. The maximum kinetic energy of the particle will be:
1. $$\frac{1}{2}m\omega^2a^2$$
2. $$\frac{5}{4}m\omega^2a^2$$
3. $$\frac{3}{2}m\omega^2a^2$$
4. Zero
Subtopic:  Energy of SHM |
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All the surfaces are smooth and springs are ideal. If a block of mass $$m$$ is given the velocity $$v_0$$ in the right direction, then the time period of the block shown in the figure will be:

1. $$\frac{12l}{v_0}$$
2. $$\frac{2l}{v_0}+ \frac{3\pi}{2}\sqrt{\frac{m}{k}}$$
3. $$\frac{4l}{v_0}+ \frac{3\pi}{2}\sqrt{\frac{m}{k}}$$
4. $$\frac{\pi}{2}\sqrt{\frac{m}{k}}$$

Subtopic:  Spring mass system |
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In a spring pendulum, in place of mass, a liquid is used. If liquid leaks out continuously, then the time period of the spring pendulum:

 1 Decreases continuously 2 Increases continuously 3 First increases and then decreases 4 First decreases and then increases

Subtopic:  Spring mass system |
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Equation of a simple harmonic motion is given by $$x= a\sin \omega t$$. For which value of $$x$$, kinetic energy is equal to the potential energy?
1. $$x = \pm a$$
2. $$x = \pm \frac{a}{2}$$
3. $$x = \pm \frac{a}{\sqrt{2}}$$
4. $$x = \pm \frac{\sqrt{3}a}{2}$$
Subtopic:  Energy of SHM |
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The displacement $$x$$ of a particle varies with time $$t$$ as $$x = A sin\left (\frac{2\pi t}{T} +\frac{\pi}{3} \right)$$$\mathrm{}$The time taken by the particle to reach from $$x = \frac{A}{2}$$ to $$x = -\frac{A}{2}$$ will be:

 1 $$\frac{T}{2}$$ 2 $$\frac{T}{3}$$ 3 $$\frac{T}{12}$$ 4 $$\frac{T}{6}$$

Subtopic:  Phasor Diagram |
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Force on a particle $$F$$ varies with time $$t$$ as shown in the given graph. The displacement $$x$$ vs time $$t$$ graph corresponding to the force-time graph will be:

 1 2 3 4
Subtopic:  Linear SHM |
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A particle executes linear SHM between $$x=A.$$ The time taken to go from $$0$$ to $$A/2$$ is $$T_1$$ and to go from $$A/2$$ to $$A$$ is $$T_2$$ then:
 1 $$T_1T_2$$ 3 $$T_1=T_2$$ 4 $$T_1= 2T_2$$
Subtopic:  Linear SHM |
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Two simple pendulums of length $$1~\text{m}$$ and $$16~\text{m}$$ are in the same phase at the mean position at any instant. If $$T$$ is the time period of the smaller pendulum, then the minimum time after which they will again be in the same phase will be:
1. $$\frac{3T}{2}$$
2. $$\frac{3T}{4}$$
3. $$\frac{2T}{3}$$
4. $$\frac{4T}{3}$$
Subtopic:  Angular SHM |
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A particle executes SHM with a time period of $$4~\text{s}$$. The time taken by the particle to go directly from its mean position to half of its amplitude will be:
1. $$\frac{1}{3}~\text{s}$$
2. $$1~\text{s}$$
3. $$\frac{1}{2}~\text{s}$$
4. $$2~\text{s}$$
Subtopic:  Linear SHM |
75%
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