Physics: amplitude, frequency, period, spring constant, max velocity and total energy

Question

A 27.8 gram mass oscillates on the end of a spring and its motion can be described by: (1.5 )sin (21.4 t ) [here the units are standard, meters and seconds] What are the following for this system: amplitude, frequency, period, spring constant, max velocity and total energy?

Answer 1

If we assume x(t)=Asin(ωt) is the position of the mass as a function of time (A=1.5m,ω=21.4 rad/sec) then

 

The amplitude A=1.5m

The frequency f=ω/2π=21.4/6.28, hz (you do the arithmetic)

The period T=1/f, sec

The spring constant k, nt/m ω²=k/M from which we get k=Mω² where M is the mass (.0278 kg)

The velocity is dx/dt=ωAcos(ωt), m/sec 

Max velocity=ωA, m/sec

Total energy E=(1/2)M(dx/dt)² + (1/2)kx², joules which when you do all the substations should be constant and expressed in terms of the initial displacement

 

Hope this helps

 

Jim