Question

A 0.55·kg mass vibrates according to the equation x = 0.44 cos (8.41t + 4.83), 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 = 0.32 m.
kinetic energy =

J
potential energy =  

J

Answer 1

Solution:

a) Amplitude = 0.44 m   

b) angular frequency = 8.41 rad/s

=> 2 x pi x v = 8.41

=> v = 1.34 Hz (approx)

c) Total energy = 0.5 m w^2 A^2 ( w is angular frequency)

E = 0.5 x 0.55 x 8.41^2 x 0.44^2

=> E = 3.77 J (approx)

d) Kinetic energy (K.E) = 0.5 m w^2 ( A^2 - x^2)

=> K.E = 0.5 x 0.55 x 8.41^2 ( 0.44^2 - 0.32^2)

=> K.E = 1.77 J

Potential energy (P. E) = 3.77 - 1.77

=> P.E = 2 J

please comment for Queries.

Please rate thanks.