In: Physics
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?
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
Vmax = A w
Vmax = (6.85) (15.91)
Vmax = 108.98 cm/s
Vmax = 1.1 m/s