A 456 g oscillator has a speed of 98.0 cm/s when its displacement is 3.00 cm...

A 456 g oscillator has a speed of 98.0 cm/s when its displacement is 3.00 cm and 69.0 cm/s when its displacement is 5.30 cm.

What is the oscillator's maximum speed?

Solutions

Expert Solution

A = amplitude of oscillations

x = displacement

w = angular frequency

v = speed of oscillator at any displacement

We know that .,

v = w sqrt(A² - x²)

oscillator has a speed of 98.0 cm/s when its displacement is 3.00 cm , so

98 = w sqrt(A² - 3²) Eq-1

oscillator has a speed of 69.0 cm/s when its displacement is 5.30 cm , so

69 = w sqrt(A² - 5.3²) Eq-2

Dividing Eq-1 by Eq-2

98/69 = w sqrt(A² - 3²) /(w sqrt(A² - 5.3²))

98/69 = sqrt(A² - 3²) /(sqrt(A² - 5.3²))

A = 6.85 cm

Using Eq-1

98 = w sqrt(A² - 3²)

98 = w sqrt(6.85² - 3²)

w = 15.91 rad/s

maximum speed is given as

V_max = A w

V_max = (6.85) (15.91)

V_max = 108.98 cm/s

V_max = 1.1 m/s

genius_generous answered 1 month ago

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