# Damped oscillation puzzle

• VishalChauhan
In summary, the conversation discusses how to find the number of oscillations it takes for a block attached to a spring to come to rest on a floor with friction. The solution involves using the conservation of energy and considering the amplitude of the block's motion. It is noted that there is no clear way to reach the solution and that exploring and playing around with different approaches is part of the learning process. The final answer for a specific set of values is 3.5 oscillations.

## Homework Statement

A block of mass m is attached to a spring of spring constant k. It lies on a floor with coefficient of friction μ. The spring is stretched by a length a and released. Find how many oscillations it takes for the block to come to rest.

## Homework Equations

d2x/dt2 + k/m x = +_ μg

Also the block will stop when the spring is unstretched and the velocity is 0

## The Attempt at a Solution

I tried to write equations for each part of the motion (ie when the frition acts along and opposite to the spring force) but its too messy. Is there another than solving the differential equation for each part of the motion.

conservation of energy?
look up the equation?

Simon Bridge said:
conservation of energy?
Thought so. But how would it give me the NUMBER of oscillations.

You can use conservation of energy to only look at the times when the block is in its extreme positions, so that you don't have to consider the change in kinetic energy. So, on any given swing, the change in stored elastic energy of the spring is equal to the work done against friction. This will tell you how much the amplitude decreases in any given swing.

Chet

Do you have the answer? If so can you please share it? I'd like to check my answer.

Try writing a sequence (if that's the correct term) for the amplitude after half-oscillations (if that makes sense).

The problem is usually given as an exercise in learning to solve problems in general.
That means that part of the learning process is going through the painful process of running into dead ends, trying other things out and so on.
There are several ways to approach the answer, you are supposed to discover one of them.

It is not as simple as getting a nice equation to plug numbers into - you do actually have to play around a bit to figure it out.

It is very common, with real problems, that you have to start out with no clear idea how the endpoint is to be reached, you should get used to it ... in this case it is not immediately obvious how to get the number of oscilations from the conservation of energy ... but as you start writing down the expressions and thinking about what you know about how energy works for this system, you'll start to see possible relationships ... like the amount of energy lost related to the distance traveled in half a swing.

BTW: you can actually use the differential equation approach you started with - I don't think there is a way through to the solution that you would consider non-messy.

Learning to play about, to explore the models you use, is the point of the exercise.

VishalChauhan
Nathanael said:
Do you have the answer? If so can you please share it? I'd like to check my answer.

Try writing a sequence (if that's the correct term) for the amplitude after half-oscillations (if that makes sense).
For m=0.5kg,friction coefficient=0.1,a=3cm and k=2.45N/cm the number of oscillations is 3.5

Nathanael

## 1. What is a damped oscillation puzzle?

A damped oscillation puzzle is a type of mechanical puzzle that involves a pendulum-like object that swings back and forth, gradually slowing down due to the effects of damping. The goal of the puzzle is to figure out how to keep the object swinging without it coming to a complete stop.

## 2. How does damping affect the motion of the object in a damped oscillation puzzle?

Damping is the process by which energy is gradually dissipated from a system, causing it to slow down. In a damped oscillation puzzle, damping causes the pendulum-like object to lose energy and eventually come to a stop.

## 3. What factors can affect the damping in a damped oscillation puzzle?

The amount of damping in a damped oscillation puzzle can be affected by various factors, such as the material and shape of the object, the surrounding air resistance, and the presence of any additional forces acting on the object.

## 4. How can I keep the object swinging in a damped oscillation puzzle?

To keep the object swinging in a damped oscillation puzzle, you need to find a way to counteract the effects of damping. This can be achieved by adding energy to the system, changing the shape or material of the object, or altering the surrounding environment.

## 5. What real-life applications does the damped oscillation puzzle have?

The damped oscillation puzzle is a simplified model of many real-life systems, such as the motion of a pendulum, a swinging door, or a swinging bridge. Understanding the principles of damping and oscillation can help in designing and maintaining these systems.