Question

a 0.60 kg mass vibrates according to the equation x=0.45 cos 6.4 t,where x is in meters and t in seconds.
Determine the
a, amplitude
b, frequency
c, total energy
d, kinetic and potential energies when x = 0.30m

Answer 1

 x=0.45 cos 6.4 t

The given is in the form of x = A cos (ωt-δ)

a)

Amplitude ,A = 0.45 m

b)

Angular velocity ω =6.4

Calculate the frequency:

f = ω/2π =6.4/2π =0.94118 s^-1

c)

Calculate the total energy by using the formula:

U = (1/2) mω²A²

  =(1/2)(0.6)(6.4)²(0.45)²

 =2.5 J

d)

Calculate the potential  energy:

PE = (1/2)mω²x²

   =(1/2)(0.6)(6.4)²(0.3)²

  =1.106 J

Calculate the kinetic energy:

KE = U-PE

      =2.5 -1.106

      =1.394 J