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Phoenix [80]
3 years ago
10

The function x = (3.0 m) cos[(4π rad/s)t + π/5 rad] gives the simple harmonic motion of a body. Find the following values at t =

3.0 s.(a) the displacementm(b) the velocity (Include the sign of the value in your answer.)m/s(c) the acceleration (Include the sign of the value in your answer.)m/s2(d) the phase of the motionrad(e) the frequency of the motionHz`(f) the period of the motions
Physics
1 answer:
just olya [345]3 years ago
5 0

Answer:

Explanation:

x  = 3 Cos (4πt + π/5)

(a) Substitute t = 3 s

x = 3 Cos (12π + π/5)

x = 3 (0.82) = 2.46 m

(b) Velocity, v = dx/dt

v = 3 (-1)(4π) Sin(4πt + π/5)

Substitute t = 3 s

v = - 37.68 Sin(12π + π/5)

v = - 37.68 (0.572)

v = - 21.55 m/s

(c) Acceleration, a = dv/dt

a = 3 (-1)(4π)(4π) Cos(4πt + π/5)

Substitute t = 3 s

a = - 473.26 (0.82)

a = - 388.21 m/s²

(d) Phase = 4πt + π/5

Substitute t = 3 s

Phase = 12 π + π/5 = 38.308 rad

(e) ω = 4π

so, 2πf = 4π

f = 2 Hz

(f) T = 1 / f = 1 / 2 = 0.5 second  

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Answer:

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According to the equation for the Balmer line spectrum of hydrogen, a value of n = 3 gives a red spectral line at 656.3 nm, a va
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Answer:

E3 = 3.03 10⁻¹⁶ kJ,  E4 = 4.09 10⁻¹⁶ kJ and  E5 = 4.58 10⁻¹⁶ kJ

Explanation:

They give us some spectral lines of the Balmer series, let's take the opportunity to place the values in SI units

     n = 3        λ = 656.3 nm = 656.3 10⁻⁹ m

     n = 4        λ = 486.1 nm = 486.1 10⁻⁹ m

     n = 5        λ=434.0 nm = 434.0 10⁻⁹ m

Let's use the Planck equation

     E = h f

The speed of light equation

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replace

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Let's calculate the energies

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    E4 = 4.09 10⁻¹⁶ kJ

n = 5

    E5 = 19.89 10⁻²⁶ /434.0 10⁻⁹

    E5 = 4.58 10⁻¹⁹ J

    E5 = 4.58 10⁻¹⁶ kJ

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