# Homework Help: Harmonic Oscillators Problems

1. Nov 11, 2009

### JJBrian

1. The problem statement, all variables and given/known data

1. A 0.5 kg mass extends a spring 1 cm. What is the frequency of oscillation of this mass
and spring?
2. A 1 m stick is used as a simple pendulum with a 3 kg weight on the end. What is its
period of oscillation?
3. The same meter stick is used as a rigid pendulum with no weight. What is its period?

2. Relevant equations

F = −kx = ma.
x = Asin(wt) .
w = sqrt(k/m)
w = 2pie/T
v = Awcos(wt) .
vmax= Aw.
a = −A^2sin(wt) .
amax= wvmax=Aw^2.
t = Ia
t = −FLsin(theta) = −mgLsin(theta) = −mgL(theta)
I = mL^2
theta = Asin((2pie/T)*t)
T = 2pie*sqrt(L/g)
2pie/T =sqrt(3g/2L)
3. The attempt at a solution

1. w = $$\sqrt{k/m}$$
w = $$\sqrt{.01m/.5kg}$$

2. T = 2*$$\pi$$ *$$\sqrt{L/g}$$
T = 2*$$\pi$$ *$$\sqrt{1m/9.8m/s^2}$$
T = 2.007 s

3. 2*$$\pi$$/T = $$\sqrt{3g/2L}$$
2*$$\pi$$/T = $$\sqrt{3(9.8)/2(1)}$$
T = 2*$$\pi$$/3.834
t = 1.6388s

Can someone check my work?