Question

A 0.55·kg mass vibrates according to the equation x = 0.41 cos (8.41t + 1.52), where x is in meters, and t is in seconds.

(a) Determine the amplitude. m

(b) Determine the frequency. Hz

(c) Determine the total energy.J

(d) Determine the kinetic energy and potential energy when x = 0.29 m.
kinetic energy = J

potential energy =  J

Answer 1

given equation is

x = 0.41 cos (8.41t + 1.52)

comparing the equation

x = A * cos(w * t + phi)

a) the amplitude is 0.41 m

b) w = 8.41 rad/s

f = w/2pi

f = 8.41/(2pi)

f = 1.34 Hz

c) total energy = 0.50 mv^2

total energy = 0.50 * 0.55 * (8.41 * 0.41)^2

total energy = 3.27 J

d)

at x = 0.29 m

as v = w * sqrt(A^2 - x^2)

v = 8.41 * sqrt(0.41^2 - 0.29^2)

v = 2.44 m/s

kinetic energy = 0.50 * 0.55 * 2.44^2

kinetic energy = 1.63 J

potential energy = 3.27 - 1.63

potential energy = 1.64 J