# The kinetic energy (K) of a simple harmonic oscillator varies with displacement (x) as shown. The period of the oscillation will be: (mass of oscillator is 1 kg)                       1. $\frac{\mathrm{\pi }}{2}$ sec 2.  $\frac{1}{2}$ sec 3.  $\mathrm{\pi }$ sec 4. 1 sec

Subtopic:  Energy of SHM |
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The equation of an SHM is given as y=3sinωt + 4cosωt where y is in centimeters. The amplitude of the SHM will be?

 1 3 cm 2 3.5 cm 3 4 cm 4 5 cm
Subtopic:  Linear SHM |
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The time periods for the figures (a) and (b) are ${\mathrm{T}}_{1}$ $\mathrm{and}$ ${\mathrm{T}}_{2}$ respectively. If all surfaces shown below are smooth, then the ratio $\frac{{\mathrm{T}}_{1}}{{\mathrm{T}}_{2}}$ will be:

1.  1: $\sqrt{3}$

2.  1: 1

3.  2: 1

4.  $\sqrt{3}$: 2

Subtopic:  Spring mass system |
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A particle is attached to a vertical spring and pulled down a distance of 0.01 m below its mean position and released. If its initial acceleration is 0.16 $\mathrm{m}/{\mathrm{s}}^{2}$, then its time period in seconds will be:

1.  $\mathrm{\pi }$

2.  $\frac{\mathrm{\pi }}{2}$

3.  $\frac{\mathrm{\pi }}{4}$

4.  $2\mathrm{\pi }$

Subtopic:  Spring mass system |
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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, ${\mathrm{y}}_{1}$ $=$ $\mathrm{a}$ $\mathrm{sin}$ $\mathrm{\omega t}$ and ${\mathrm{y}}_{2}$ $=$ $2\mathrm{a}$ $\mathrm{sin}\left(\mathrm{\omega t}\right)$ $+$ $\frac{2\mathrm{\pi }}{3}$  are superimposed on a particle of mass m. The maximum kinetic energy of the particle will be:

1.  $\frac{1}{2}{\mathrm{m\omega }}^{2}{\mathrm{a}}^{2}$

2.  $\frac{5{\mathrm{m\omega }}^{2}{\mathrm{a}}^{2}}{4}$

3.  $\frac{3}{2}{\mathrm{m\omega }}^{2}{\mathrm{a}}^{2}$

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 = asin$\mathrm{\omega }$t. For which value of x, kinetic energy is equal to the potential energy?

1.  $\mathrm{x}$ $=$ $±$ $\mathrm{a}$

2.  $\mathrm{x}$ $=$ $±$ $\frac{\mathrm{a}}{2}$

3.  $\mathrm{x}$ $=$ $±$ $\frac{\mathrm{a}}{\sqrt{2}}$

4.  $\mathrm{x}$ $=$ $±$ $\frac{\sqrt{3}\mathrm{a}}{2}$

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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