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

In summary, the conversation discusses a 3.0kg mass connected to a system of three springs with different spring constants. Part (a) asks for the relation between the spring constants and the equivalent spring constant of the three springs together. Part (b) asks for the speed of the mass when released from a 10cm displacement, and part (c) asks for the time it takes for the mass to complete 4.00 cycles of motion. The solution to part (a) is 1/k1 + 1/k2 + 1/k3 = 1/keff, which gives a keff value of 34.28 N/m. For part (b), energy concepts can be used to determine the mass

## 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?

Last edited:

## 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?

berkeman said:
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

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

haruspex said:
Thank you very much!

## 1. What is an oscillating system?

An oscillating system is a physical system that exhibits periodic motion. This means that the system repeats the same motion over and over again, typically in a back-and-forth or up-and-down fashion.

## 2. What are some examples of oscillating systems?

Some examples of oscillating systems include a pendulum, a spring-mass system, a vibrating guitar string, and a swinging door.

## 3. How do different oscillating systems behave differently?

Different oscillating systems behave differently depending on their specific properties. For example, a pendulum will have a different period (time for one full swing) depending on its length, while a spring-mass system will have a different period depending on the mass attached to the spring.

## 4. How is the behavior of an oscillating system described?

The behavior of an oscillating system is typically described using concepts such as amplitude, frequency, and period. Amplitude refers to the maximum displacement from the equilibrium position, frequency refers to the number of oscillations per unit time, and period refers to the time for one full oscillation.

## 5. What are some real-world applications of oscillating systems?

Oscillating systems are used in a variety of real-world applications, such as timekeeping (e.g. pendulum clocks), music (e.g. guitar strings), and engineering (e.g. earthquake-resistant buildings). They are also important in fields like physics and engineering for understanding and analyzing motion and vibrations.

• Introductory Physics Homework Help
Replies
19
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Mechanics
Replies
10
Views
842
• Introductory Physics Homework Help
Replies
5
Views
3K
• Introductory Physics Homework Help
Replies
2
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
311
• Introductory Physics Homework Help
Replies
11
Views
336
• Introductory Physics Homework Help
Replies
4
Views
928
• Introductory Physics Homework Help
Replies
2
Views
1K
• Programming and Computer Science
Replies
15
Views
2K