Answer to Question #116668 in Mechanics | Relativity for fiona

Question

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.

Answer 1

$$E=0.5kA^2=0.5mV^2=0.5kx^2+0.5mv^2$$

$$0.5mv^2=\frac{9^2}{16^2}E=0.5kA^2\frac{9^2}{16^2}$$

$$A^2=x^2+A^2\frac{9^2}{16^2}\to 8^2=x^2+8^2\frac{9^2}{16^2}$$

$$x=6.6\ m$$