# Spring oscillations determining period of motion

1. Dec 3, 2011

### biga415

Hey guys, i cant figure this one out.

a mass attached to a spring oscillates with an amplitude of 18cm; the spring constant is k=18N/m. when the position is half the maximum value, the mass moves with velocity v=27cm/s.
a) determine the period of motion.

b)find the value of mass

i tried to find the mass first but that didnt work. i used kinematics, T= 2∏/ω, ω=sqrt(m/k) and T= 2∏sqrt(m/k) but none of them were working.

thanks for the help!

2. Dec 3, 2011

### Curl

Is this a damped system or undamped?

If it is undamped, then the amplitude of oscillation is irrelevant, and the frequency is sqrt(k/m). Find m from the kinetic energy of the mass. You know how much the energy is because you know the work done by the spring during half of the amplitude.

P.S. You also know it will be a sine wave for an undamped system, and you know the amplitude of the wave and derivative at a point. You can calculate it that way too if you'd like.