Period of oscillation for a mass on a spring

[andycl]

A mass which is resting on a horizontal frictionless surface is connected to a fixed spring. The mass is displaced 0.16 m from its equilibrium position and released. At t = 0.50 s, the mass is 0.08 m from its equilibrium position (and has not passed through it yet).

What is the period of oscillation of the mass?

I know I am suppose to put what I have done so far but I have given up with the trying. Could somebody please give me some guidance and explain please.

Thank you!

 

[Dick]

You can generally write the position of the mass wrt to equilibrium as x(t)=A*cos(omega*t+phi), where A is the maximum displacement and phi is the phase. Since you know you have maximum displacement at t=0 you can set phi=0 and A=0.16m. So x(t)=(0.16m)*cos(omega*t). Enough hints, now can you put the values at t=0.5 sec in and solve for omega? Knowing omega, can you figure out the period?