# Period of a mass oscillating on a spring

• jgens
In summary, the conversation discussed the period of a mass oscillating on a Hookeian spring and the equations used to find it. The correct solution was given using integration, while a simpler solution was also mentioned using the equation F = ma = -kx. The period was found to be T = 2pi/w, where w = sqrt(k/m).
jgens
Gold Member

## Homework Statement

The period of a mass m oscillating on a hookian spring of negligible mass.

F = -kx

## The Attempt at a Solution

I'm using x in place of ∆x for convienance.

F = -kx

dv/dt = -kx/m

∫vdv = -k/m∫xdx

v^2 = C - k(x^2)/m: Placing the restraint that if v = 0, x = xi

v^2 = k(xi^2)/m - k(x^2)/m

v = sqrt(k(xi^2)/m - k(x^2)/m)

t = sqrt(m/k)∫dx/sqrt(xi^2 - x^2)

t = arcsin(x/xi)sqrt(m/k). Therefore, if we allow ∆x = 0

t = arcsin(0)sqrt(m/k). Hence, if we want the time for one period:

t = 2pisqrt(m/k)

Is this correct? Thanks!

Yes that is correct.
But if you didn't want to integrate you could have just put F=ma=-kx
such that a= -(k/m)x
which is in the form a=-(w^2)x meaning that w=sqrt(k/m)

and the period T=2pi/w

Thanks! That's a much simpler derivation.

## What is the period of a mass oscillating on a spring?

The period of a mass oscillating on a spring is the time it takes for the mass to complete one full cycle of oscillation, returning to its original position and velocity.

## What factors affect the period of a mass oscillating on a spring?

The period of a mass oscillating on a spring is affected by the mass of the object, the spring constant, and the amplitude of the oscillation.

## How is the period of a mass oscillating on a spring calculated?

The period of a mass oscillating on a spring can be calculated using the formula T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant.

## Can the period of a mass oscillating on a spring be changed?

Yes, the period of a mass oscillating on a spring can be changed by altering the mass, spring constant, or amplitude of oscillation.

## What is the relationship between the period and frequency of a mass oscillating on a spring?

The period and frequency of a mass oscillating on a spring are inversely related. The period is equal to 1/frequency, or T = 1/f.

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