# A particle moves according to the law, $\mathrm{x}=\mathrm{r}$ $\mathrm{cos}\frac{\mathrm{\pi t}}{2}$. The distance covered by it in the time interval between t =0 to t =3 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 |
67%
From NCERT
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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 (in J) of a body executing SHM is given by U = 20 + 10 (${\mathrm{sin}}^{2}$100$\mathrm{\pi }$t), then the minimum potential energy of the body will be:

 1 Zero 2 30 J 3 20 J 4 40 J
Subtopic:  Energy of SHM |
72%
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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 $\frac{\mathrm{\pi }}{2}$ sec 2 $\frac{1}{2}$ sec 3 $\mathrm{\pi }$ sec 4 1 sec
Subtopic:  Energy of SHM |
75%
From NCERT
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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 |
90%
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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 |
81%
From NCERT
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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 |
88%
From NCERT
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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 |
55%
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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 |
58%
From NCERT
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