Final answer:
The amplitude is 0.45 meters, the frequency is approximately 1.02 Hz, the total energy cannot be determined, and the kinetic and potential energies can be calculated using the given equation.
Step-by-step explanation:
To determine the amplitude, frequency, total energy, and kinetic and potential energies, we will use the given equation x = 0.45cos(6.40t).
a) The amplitude (A) is equal to the coefficient of the cosine function, so A = 0.45 meters.
b) The angular frequency (ω) is the coefficient of t in the cosine function, so ω = 6.40 radians/second. The frequency (f) can be calculated using the formula f = ω / (2π), giving a frequency of approximately 1.02 Hz.
c) The total energy (E) of the system can be calculated using the formula E = 0.5kA^2, where k is the spring constant. Since the equation does not provide information about the spring constant, we cannot determine the total energy.
d) To find the kinetic and potential energies when x = 0.3 m, we need to substitute this value into the equation and calculate the corresponding values. The kinetic energy (K) can be calculated using the formula K = 0.5mv^2, where m is the mass and v is the velocity. The potential energy (U) can be calculated using the formula U = 0.5kx^2.