How Do You Calculate the Speed of a Mass in an Oscillating System?

[Adriano25]

Homework Statement

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

Homework Equations

I solved part a)
1/k1 + 1/k2 + 1/k3 = 1/keff

keff = 34.28 N/m

The Attempt at a Solution

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

 

[berkeman]

Homework Statement

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?
View attachment 110189

Homework Equations

I solved part a)
1/k1 + 1/k2 + 1/k3 = 1/keff

keff = 34.28 N/m

The Attempt at a Solution

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

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

 

[Adriano25]

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

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

 

[haruspex]

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

Think about energy.

 

[Adriano25]

Think about energy.

Thank you very much!