Question

13.9 An 8 kg mass is attached to a spring with a spring constant of 750 N/m. As the mass passes a position x, the speed is 2.75 m/s and the potential energy is 8.6 J. a) What is the amplitude? b) What is the maximum speed? c) What is the energy of the system? d) What was the value of 2.75 m/s x-0 x-?

please write out work (not typed)

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Answer 1

Mass m = 8 kg spring constant K = 750 N/m Angular frequency w = squareroot K/m w = squareroot 750 N/m/8 Kg W = 9.68 rad/s we will determine 'x' Given at X^2, Potential Energy U = 8.6 J Potential Energy in SHM U = 1/2 KX^2 p.6 = 1/2 times 750 N/m X^2 X^2 = 0.022 gm^2 x = 0.151 m \r\n Amplitude A = 2 In SHM motion speed V = W squareroot A^2 - X^2 Given V = 2.75 m/s, w = 9.68 rad/s (calculated) x = 0.151 m Putting these values 2.75 m/s = 9.68 rad/s squareroot A^2 - (0.151 m)^2 A = 0.321 m = 32 Km Maximum Speed v = AW V_max = 0.321 m times 9.68 rad/s V_max = 3.10 m/s Energy of system E = 1/2 mw^2 A^2 E = 1/2 times 8 kg times (9.68 rad/s)^2 times (0.321 m) E = 38.44 Joule X calculated x = 0.151 m = 15.1 cm