# Oscillations, calculating spring constant, amplitude, period

1. May 17, 2014

### selsunblue

1. The problem statement, all variables and given/known data
A spring stretches 0.150m when a 0.300kg object is hung from it. The spring is then stretched an additional 0.100m from this equilibrium point and released.

A) Calculate the spring constant (k)

B) Calculate the amplitude, period of motion T, frequency f and angular velocity ω

C) Find the maximum magnitude of the velocity, vmax and indicate the positions that it occurs on your sketch

D) Find the maximum magnitude of the acceleration and indicate the positions that it occurs on your sketch.

2. Relevant equations
Hooke's law, F=mg=kx
ω=sqrt(k/m)
T=2∏/ω = 2∏ * sqrt(m/k)
f=ω/2∏
ω=sqrt(k/m)

3. The attempt at a solution
A) k=f/x=mg/x=(0.300)(9.80)/0.150 = 19.6 N/m

B) amplitude=0.100
T=0.777
f=1.3
ω=8.08

C) 1/2 *mv^2 = 1/2 * kA^2
v=A*sqrt(k/m)=0.808 m/s

Is this value for C correct?

D) a=kA/m = (19.6*0.100)/0.300 = 6.53 m/s^2

2. May 17, 2014

### dauto

All seems correct.