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alexandr402 [8]
2 years ago
8

The motion of a particle connected to a spring is described by x = 10 sin (pi*t). At

Physics
1 answer:
Gekata [30.6K]2 years ago
6 0

To solve this problem we will first apply the principle of energy conservation, for which the elastic potential energy must be the same as the elastic kinetic energy of the simple harmonic movement of the system.

From this conservation it will be possible to find in total terms the total displacement of the system and thus replace it in the given function to find the time.

The potential energy stored would be

PE= \frac{1}{2} kx^2

The kinetic energy would be

KE = \frac{1}{2}m\omega (A^2-x^2)

Here,

A = 10m

\omega = \pi rad/s

Now assuming the planned conservation of energy

PE = KE

\frac{1}{2}kx^2 =\frac{1}{2} m\omega^2 (A^2-x^2)

\frac{1}{2}kx^2 = \frac{1}{2} m(x\frac{k}{m})(A^2-x^2)

x^2 = A^2 -x^2

2x^2 = A^2

x = \frac{A}{\sqrt{2}}

x = \frac{10}{\sqrt{2}}

So now using the equation previously given to describe the motion of the particle we have to

\frac{10}{\sqrt{2}} = 10 sin(xt)

\frac{1}{\sqrt{2}} = sin (xt)

sin^{-1} (\frac{1}{\sqrt{2}} ) = \pi t

\frac{\pi}{4} = \pi t

t = \frac{1}{4}s= 0.25s

Therefore the correct option is B.

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FrozenT [24]

Answer:

5.5 × 10^14 Hz or s^-1

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Explanation:

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6.63 × 10 ^-34 × f0 = 6.63 × 10 ^-34× 6.66 × 10^14 - 7.74× 10^-20

6.63 × 10 ^-34 × f0 = 3.64158×10^-19

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2 years ago
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Answer:

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