Answer to Question #116668 in Mechanics | Relativity for fiona

Question #116668
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
Expert's answer
2020-05-19T10:49:52-0400
E=0.5kA2=0.5mV2=0.5kx2+0.5mv2E=0.5kA^2=0.5mV^2=0.5kx^2+0.5mv^2

0.5mv2=92162E=0.5kA2921620.5mv^2=\frac{9^2}{16^2}E=0.5kA^2\frac{9^2}{16^2}

A2=x2+A29216282=x2+8292162A^2=x^2+A^2\frac{9^2}{16^2}\to 8^2=x^2+8^2\frac{9^2}{16^2}

x=6.6 mx=6.6\ m


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