# Oscillations, calculating spring constant, amplitude, period

## Homework Statement

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.

## Homework 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)

## 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