# Special Relativity and SHM

• PsychonautQQ
In summary: The reason for this is because in the rest frame of the person moving with the system, the spring is at equilibrium and so the oscillations are minimal. However, when the observer watches the system from a different reference frame, the spring is still moving and so the oscillations are larger.

## Homework Statement

an observer see's a system consisting of a spring and mass in SHM move past them and measures the period of oscillation to be T. What will a second observer riding with the system see the period as T as?

γ*proper time = time.

so the person moving along with the system is viewing the proper time, and therefore the person looking on from outside will be viewing the time that is INCREASED. so the person riding with the system will see a smaller period than the person observing the system from the outside.
That is what I came up with qualitatively. However the demon that was bothering me regarding this question is does length contraction come into play here to balance the equations out? I figure since T is measure in units of seconds I could just use the time dilation equation, but does the fact that one person see's the oscilliation moving a further distance than the other make a difference?

Is the idea that the person riding along with the system will perceive a shorter time of oscillation than the person watching in a different reference frame?

The problem statement says "a second observer riding with the system" but I don't think you're supposed to interpret that as a rest frame for the entire system. First that would require that all points of the spring are accelerating at the same rate, otherwise the notion of a rest frame for the entire system has no meaning because different points of the spring would have different instantaneous rest frames; keep in mind that in SR, a body with constituent points that all have the same acceleration cannot be rigid. Secondly, if we were indeed in such a rest frame of the entire system then the system would be at rest so what oscillations are there to even measure? So I take it what's being referred to is the rest frame of e.g. the equilibrium position; finally when you mention length contraction do you mean something along the lines of length contraction of the equilibrium position?

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Yes that's what I mean when I say length contraction. The main question is just how will the periods of observations compare for the two people (one in the same reference frame that's moving with the spring mass system and one that is watching from a reference frame where that one is moving). I think the person that is riding in the same reference frame as the mass-spring system will see a shorter period of oscillation than the other observer.

## What is special relativity?

Special relativity is a theory developed by Albert Einstein that describes the behavior of objects moving at constant speeds in the absence of external forces. It states that the laws of physics are the same for all observers in uniform motion and that the speed of light is constant for all observers.

## What is the difference between special relativity and general relativity?

Special relativity deals with the behavior of objects in inertial reference frames, while general relativity deals with the behavior of objects in non-inertial reference frames, including those affected by gravity.

## What is SHM?

SHM stands for simple harmonic motion, which is a type of periodic motion in which the restoring force is directly proportional to the displacement from equilibrium. Examples of SHM include a swinging pendulum or a mass on a spring.

## How is special relativity related to SHM?

In special relativity, time is relative and is affected by the speed of an object. This can have an impact on the perceived frequency of an object in SHM. For example, an observer moving at high speeds relative to a pendulum will perceive the pendulum to be moving at a slower frequency.

## What are some practical applications of special relativity and SHM?

Special relativity is used in many modern technologies, including GPS systems and particle accelerators. SHM is used in the design of many mechanical systems, such as clocks and watches, as well as in musical instruments and earthquake-resistant buildings.