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sergey [27]
3 years ago
7

Question 8

Physics
1 answer:
viktelen [127]3 years ago
3 0

Answer: D(t) = 8.e^{-0.4t}.cos(\frac{\pi }{6}.t )

Explanation: A harmonic motion of a spring can be modeled by a sinusoidal function, which, in general, is of the form:

y = a.sin(\omega.t) or y = a.cos(\omega.t)

where:

|a| is initil displacement

\frac{2.\pi}{\omega} is period

For a Damped Harmonic Motion, i.e., when the spring doesn't bounce up and down forever, equations for displacement is:

y=a.e^{-ct}.cos(\omega.t) or y=a.e^{-ct}.sin(\omega.t)

For this question in particular, initial displacement is maximum at 8cm, so it is used the cosine function:

y=a.e^{-ct}.cos(\omega.t)

period = \frac{2.\pi}{\omega}

12 = \frac{2.\pi}{\omega}

ω = \frac{\pi}{6}

Replacing values:

D(t)=8.e^{-0.4t}.cos(\frac{\pi}{6} .t)

The equation of displacement, D(t), of a spring with damping factor is D(t)=8.e^{-0.4t}.cos(\frac{\pi}{6} .t).

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Plugging in the values gives, q' = 0.307 W per m²

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