# The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:                  1. 25 Hz 2. 50 Hz 3. 12.25 Hz 4. 33.3 Hz

Subtopic:  Simple Harmonic Motion |
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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 |
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Two equations of S.H.M. are ${\mathrm{y}}_{1}=\mathrm{asin}\left(\mathrm{\omega t}-\mathrm{\alpha }\right)$ and ${\mathrm{y}}_{2}=\mathrm{bcos}\left(\mathrm{\omega t}-\mathrm{\alpha }\right)$. The phase difference between the two is:
1. $$0^\circ$$
2. $$\alpha^\circ$$
3. $$90^\circ$$
4. $$180^\circ$$

Subtopic:  Simple Harmonic Motion |
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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 |
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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 |
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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 |
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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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