# Variety of Oscillating systems

1. Dec 9, 2016

1. The problem statement, all variables and given/known data
A 3.0kg mass is connected to a system of three springs, k1 = 100N/m, k2 = 80N/m, and k3 = 150N/m, as shown below.
(a) Derive the relation between k1, k2, k3 and the equivalent spring constant of the three springs together.
(b) If the mass is pulled 10cm from its equilibrium position and released from rest, what is its speed when it returns to the equilibrium position?
(c) How much time does it take the mass to complete 4.00 cycles of motion

2. Relevant equations
I solved part a)
1/k1 + 1/k2 + 1/k3 = 1/keff

keff = 34.28 N/m

3. The attempt at a solution

I just have no idea how to start on part b). Any thoughts please?

Last edited: Dec 9, 2016
2. Dec 9, 2016

### Staff: Mentor

We generally don't allow "I have no idea" on schoolwork problems here. Have you worked any problems yet with springs and masses oscillating?

3. Dec 9, 2016

Yes. I was only able to find the angular frequency:
ω=sqrt(keff/m)
ω= 3.38 s-1

4. Dec 9, 2016