Simple harmonic motion Quiz 1

Question 1

If the total energy of a body which oscillates simple harmonically is $$0.05	ext{ J}$$, frequency of oscillating body is given by $$($$Take mass and acceleration of the body to be $$2 g$$ and $$2 ms^{-2}$$ respectively$$)$$

Accepted Answer

$$\sqrt{0.317}	ext{ Hz}$$

Answer

$$\sqrt{0.217}	ext{ Hz}$$

Answer

$$\sqrt{0.313}	ext{ Hz}$$

Answer

$$\sqrt{0.414}	ext{ Hz}$$

Question 2

Consider an object which undergoes simple harmonic motion. If the angular frequency of this object is given by $$\dfrac{\pi }{2}	ext{ secon}{{	ext{d}}^{-1}}$$ and if the velocity of this object for a shift of $$5	ext{ m}$$ is $$0.6	ext{ m}{{	ext{s}}^{-1}}$$, the velocity of this particle for a shift of $$7	ext{ m}$$ is

Accepted Answer

$$\sqrt{0.36-6{{\pi }^{2}}}$$

Answer

$$\sqrt{0.63-6{{\pi }^{2}}}$$

Answer

$$\sqrt{0.36-3{{\pi }^{2}}}$$

Answer

$$\sqrt{0.63-3{{\pi }^{2}}}$$

Question 3

The type of motion of a particular particle is understood to be simple harmonic motion. If the motion of this particle has an amplitude of $$0.2	ext{ m}$$, determine the shift in position of the particle when its velocity is $$0.1	ext{ m}{{	ext{s}}^{-1}}$$. Given that shift in its position is $$0.4	ext{ m}$$ when it has a velocity of $$0.4	ext{ m}{{	ext{s}}^{-1}}$$.

Accepted Answer

$$0.217	ext{ m}{{	ext{s}}^{-1}}$$

Answer

$$0.71	ext{2m}{{	ext{s}}^{-1}}$$

Answer

$$0.127	ext{ m}{{	ext{s}}^{-1}}$$

Answer

None of these

Question 4

What would have been the square of velocity of a body at a dislocation of $$0.6	ext{ m}$$ if it had a velocity of $$0.6	ext{ m}{{	ext{s}}^{-1}}$$ at a dislocation of $$0.2	ext{ m}$$ and if the time period of oscillation of the body was represented $$T$$? $$($$Consider the body to be carrying out simple harmonic motion$$)$$

Accepted Answer

$$0.36-\dfrac{0.32}{{{T}^{2}}}$$

Answer

$$\dfrac{0.38}{{{T}^{2}}}-0.44$$

Answer

$$\dfrac{0.62}{{{T}^{2}}}-0.18$$

Answer

$$0.24-\dfrac{0.48}{{{T}^{2}}}$$

Question 5

If the liquid level in one limb of a manometer $$($$U-shaped$$)$$ goes up by _ , the liquid level in the other limb of the tube does down by $$0.4	ext{ m}$$, which makes the difference in levels of liquid in the tube to be _ . The angular frequency of oscillations in this case is given by _ . $$($$Take area of cross-section of the tube to be $$\,0.1	ext{ }{{	ext{m}}^{2}},$$ mass of the liquid to be $$\,200	ext{ g}$$ and density of the liquid to be $${{10}^{3}}	ext{ kg}{{	ext{m}}^{-3}})$$

Accepted Answer

$$0.4	ext{ m ; 0}	ext{.8 m ; 95 rad/s}$$

Answer

$$0.8	ext{ m ; 0}	ext{.4 m ; 74 rad/s}$$

Answer

$$0.2	ext{ m ; 0}	ext{.2 m ; 62 rad/s}$$

Answer

$$0.6	ext{ m ; 0}	ext{.2 m ; 57 rad/s}$$