Physics Quetion

Question

A 0.46 kg mass vibrates according to the equation x = 0.48 cos 8.37t, where x is in meters, and t is in seconds. (a) Determine the amplitude. 0.48 m (b) Determine the frequency. Hz (c) Determine the total energy. J (d) Determine the kinetic energy and potential energy when x = 0.28 m. kinetic energy J potential energy J

Answer 1

(a)

 

x_max = 0.48 m

 

(b)

 

ω = 8.37 rad/s

f = ω/(2π) = 8.37/(2π) Hz = 1.33 Hz

 

(c)

 

E = (1/2)kx_max²

k = mω² = (0.46)(8.37)² N/m = 32.23 N/m

E = (1/2)(32.23)(0.48)² J = 3.71 J

 

(d)

 

U = (1/2)kx² = (1/2)(32.23)(0.28)² J = 1.26 J

K = E - U = (3.71 - 1.26) J = 2.45 J