# The variation of the potential energy of the harmonic oscillator is shown in the figure. The spring constant will be:             1. $$1\times10^{2}~\text{N/m}$$ 2. $$150~\text{N/m}$$ 3. $$0.667\times10^{2}~\text{N/m}$$ 4. $$3\times10^{2}~\text{N/m}$$

Subtopic:  Energy of SHM |
62%
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A particle moves according to the law $$x= r\cos\left(\frac{\pi t}{2}\right)$$. The distance covered by it in the time interval between $$t=0$$ to $$t=3~\text{s}$$ will be:
 1 $$r$$ 2 $$2r$$ 3 $$3r$$ 4 $$4r$$
Subtopic:  Linear SHM |
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A mass of 30 g is attached with two springs having spring constant 100 N/m and 200 N/m and other ends of springs are attached to rigid walls as shown in the given figure. The angular frequency of oscillation will be

1.  $\frac{100}{2\mathrm{\pi }}$ $\mathrm{rad}/\mathrm{s}$

2.  $\frac{100}{\mathrm{\pi }}$ $\mathrm{rad}/\mathrm{s}$

4.  200$\mathrm{\pi }$ rad/s

Subtopic:  Combination of Springs |
68%
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If a particle in SHM has a time period of $$0.1$$ s and an amplitude of $$6$$ cm, then its maximum velocity will be:
1. $$120 \pi$$$\mathrm{}$ cm/s

2. $$0.6 \pi$$$\mathrm{}$ cm/s

3. $$\pi$$$\mathrm{}$ cm/s

4. $$6$$ cm/s

Subtopic:  Simple Harmonic Motion |
90%
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If the potential energy $$U$$ $$(\text{in J})$$ of a body executing SHM is given by $$U = 20+ 10(\sin^2 100\pi t),$$ then the minimum potential energy of the body will be:
 1 Zero 2 $$30~\text{J}$$ 3 $$20~\text{J}$$ 4 $$40~\text{J}$$
Subtopic:  Energy of SHM |
72%
From NCERT
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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. $$\frac{\pi}{2}~\text{s}$$
2. $$\frac{1}{2}~\text{s}$$
3. $$\pi~\text{s}$$
4. $$1~\text{s}$$

Subtopic:  Energy of SHM |
75%
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The equation of an SHM is given as $$y = 3\sin\omega t+ 4\cos \omega t$$ where $$y$$ is in centimeters. The amplitude of the SHM will be?
 1 $$3~\text{cm}$$ 2 $$3.5~\text{cm}$$ 3 $$4~\text{cm}$$ 4 $$5~\text{cm}$$
Subtopic:  Linear SHM |
90%
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The time periods for the figures (a) and (b) are $$T_1$$ and $$T_2$$ respectively. If all surfaces shown below are smooth, then the ratio $$\frac{T_1}{T_2}$$ will be:

1. $$1:\sqrt{3}$$
2. $$1:1$$
3. $$2:1$$
4. $$\sqrt{3}:2$$
Subtopic:  Spring mass system |
82%
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A particle is attached to a vertical spring and pulled down a distance of $$0.01~\text{m}$$ below its mean position and released. If its initial acceleration is $$0.16~\text{m/s}^2$$, then its time period in seconds will be:
1. $$\pi$$
2. $$\frac{\pi}{2}$$
3. $$\frac{\pi}{4}$$
4. $$2\pi$$
Subtopic:  Spring mass system |
88%
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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 |
56%
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