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Dennis_Churaev [7]
2 years ago
9

An object moves in simple harmonic motion described by the equation d equals one fifth sine 2 t where t is measured in seconds a

nd d in inches. Find the maximum​ displacement, the​ frequency, and the time required for one cycle.
Physics
1 answer:
tensa zangetsu [6.8K]2 years ago
3 0

Answer:

The maximum​ displacement, the​ frequency, and the time required for one cycle are 1/5 inch, 1/π Hz and π sec.

Explanation:

Given that,

The equation of simple harmonic motion

d = \dfrac{1}{5}\sin 2t.....(I)

We need to calculate the maximum amplitude

Using equation of simple harmonic motion

y = a \sin\omega t

Where, a = amplitude

\omega =frequency

t = time

On comparing equation (I) and general equation

The amplitude is a maximum displacement traveled by a wave.

a = \dfrac{1}{5}

So, the maximum displacement is

d= \dfrac{1}{5}\ inch

We need to calculate the frequency

\omega=2\pi f

f = \dfrac{1}{\pi}\ Hz

We need to calculate the time required for one cycle

t =\dfrac{1}{f}

t =\pi\ sec

Hence, The maximum​ displacement, the​ frequency, and the time required for one cycle are 1/5 inch, 1/π\ Hz and π\ sec.

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