A 0.500 kgmass on a spring has velocity as a function of timegiven by v(t) = -(2

Question

A 0.500 kgmass on a spring has velocity as a function of timegiven by v(t) = -(2.85m/s)sin[(15.5s^-1)t –/2].Determine the following quantities:
(a) The oscillation frequency fof the mass. (b) The spring constant (k) of the spring. (c) The max. x-position of the mass. (d) The max. kinetic energy of the mass. (e) The max. elastic pot. energy of the spring. A 0.500 kgmass on a spring has velocity as a function of timegiven by v(t) = -(2.85m/s)sin[(15.5s^-1)t –/2].Determine the following quantities:
(a) The oscillation frequency fof the mass. (b) The spring constant (k) of the spring. (c) The max. x-position of the mass. (d) The max. kinetic energy of the mass. (e) The max. elastic pot. energy of the spring.

Explanation / Answer

a) The frequency of the spring is               f = /(2)                 = (15.5 /s)/(2) b) The spring constant is            k = m ^2               = (0.500 kg)(15.5 rad/s)^2 c) The max x- position of the mass is                 A = (2.85 m/s)/(15.5 /s) d) The max . kinetic energy is                 Kmax = (1/2)mvmax2 Here m = 0.500 kg          vmax = 2.85 m/s e) The max. elastic potential energy of the spring is                 U = (1/2)kA2 Substitute the values.

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