A particle attached to a spring with k = 51 N/m is undergoing simple harmonic mo

Question

A particle attached to a spring with k = 51 N/m is undergoing simple harmonic motion, and itsposition is described by the equation x = (6.0 m)cos(8.1t),with t measured in seconds. (a) What is the mass of the particle?
1 kg

(b) What is the period of the motion?
2 s

(c) What is the maximum speed of the particle?
3 m/s

(d) What is the maximum potential energy?
4 J

(e) What is the total energy?
5 J (a) What is the mass of the particle?
1 kg

(b) What is the period of the motion?
2 s

(c) What is the maximum speed of the particle?
3 m/s

(d) What is the maximum potential energy?
4 J

(e) What is the total energy?
5 J

Explanation / Answer

Spring constant k = 51 N / m position x = (6.0m)cos(8.1t) compare this with x = A cos ( wt ) we get amplitude A = 6 m angular frequency w = 8.1 rad /s      (a). the mass of the particle m = [ k / w ^ 2 ]                                             = 0.777 kg                                             


(b) the period of the motion T = 2 / w                                             = 0.7757 s


(c) the maximum speed of the particle v = A w                                                             = 48.6 m / s


(d) the maximum potential energy P = ( 1/ 2) k A ^2
                                                      = 918 J

(e) the total energy E = 918 J

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