Answer to Question #116668 in Mechanics | Relativity for fiona
2020-05-17T07:03:32-04:00
The amplitude of a spring-mass system in simple harmonic motion is 8 m. Calculate the value of
displacement x where the magnitude of the velocity is 9/16 of its maximum value.
1
2020-05-19T10:49:52-0400
E = 0.5 k A 2 = 0.5 m V 2 = 0.5 k x 2 + 0.5 m v 2 E=0.5kA^2=0.5mV^2=0.5kx^2+0.5mv^2 E = 0.5 k A 2 = 0.5 m V 2 = 0.5 k x 2 + 0.5 m v 2
0.5 m v 2 = 9 2 1 6 2 E = 0.5 k A 2 9 2 1 6 2 0.5mv^2=\frac{9^2}{16^2}E=0.5kA^2\frac{9^2}{16^2} 0.5 m v 2 = 1 6 2 9 2 E = 0.5 k A 2 1 6 2 9 2
A 2 = x 2 + A 2 9 2 1 6 2 → 8 2 = x 2 + 8 2 9 2 1 6 2 A^2=x^2+A^2\frac{9^2}{16^2}\to 8^2=x^2+8^2\frac{9^2}{16^2} A 2 = x 2 + A 2 1 6 2 9 2 → 8 2 = x 2 + 8 2 1 6 2 9 2
x = 6.6 m x=6.6\ m x = 6.6 m
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