# Oscillations and waves

1. Oct 18, 2010

### ruppy99

Ok first time poster here so I hope I do this right. 2 assignment q's out of four I got I'm having trouble with. I think there might be missing info but I'm hoping for someone to back me up on this or to point me in the right direction.

1. The problem statement, all variables and given/known data
Q.1
Consider two identical ideal springs with a mass m attached which are harmonically
oscillating out of phase relative to each other, with the spring constant k = 100 Nm-1
and the mass m = 10-3 kg.
At the time t0 = + 0.1 sec the displacement of the spring 1 is x1(t0) = 10 mm and the
displacement of spring 2 is x1(t0) = 1 mm.
(i) Calculate the value of the amplitude A of each oscillation.
(ii) Calculate the value of the phase-difference φ between the two oscillators.

Q.2
The potential energy stored in a harmonic oscillator at time t0 = -0.5 s is 1 mJ. The
spring-constant associated with the oscillator has the value k = 103 N m-1 and the
oscillation amplitude is A = 10-6 m.
Calculate the magnitude of the maximum acceleration.

2. Relevant equations
Q.1
$$\omega$$=$$\sqrt{k/m}$$
f=$$\omega$$/2pi
T=1/f
Q.2
1/2mv2+1/2kx2=total energy in harmonic oscillator

3. The attempt at a solution
Q.1
Found $$\omega$$=316.23 rad/s, f=50.33hz and T=0.0199 yhen got stuck and wondered is there enough info..
Q.2
found total energy=0.005J, Kinetic energy at that point=0.004J and the x=1.41X10-3m