A 60 kg mass vibrates according to the equation x=0.45 cos6.40t, where x is in meters and t is in seconds. Determine (a) the amplitude (b) the frequency (c) the kinetic energy and potential energies when x = .30 m

I'm guessing that the formula is supposed to resemble x= A cos wt?? I don't know how I would determine these answers with this formula. Is the unit for amplitude supposed to be meters?

Question

A 60 kg mass vibrates according to the equation x=0.45 cos6.40t, where x is in meters and t is in seconds. Determine (a) the amplitude (b) the frequency (c) the kinetic energy and potential energies  when x = .30 m

I'm guessing that the formula is supposed to resemble x= A cos wt?? I don't know how I would determine these answers with this formula. Is the unit for amplitude supposed to be meters?

anonymous · Answer

It does resemble x=Acos(wt). Cosine function works only on values with no units (no sense in cos(2 cm)) and the answer also has no units. So, since x is in meter, the amplitude is 0.45 m. 
To find frequency, divide w with 2*pi. Since t is in seconds, w has to have the unit of $$s ^{-1}$$

anonymous · Answer

To find KE and PE, you'll need to find the spring constant by using the relation $$\omega=(k/m)^{\frac{1}{2}}$$
You can find the KE by finding the velocity function (differentiate x=Acoswt) and then to find PE, remove KE from total energy.