Amplitude and period harmonic motion

[pb23me]

Homework Statement

Im confused about what exactly is the period and amplitude of a spring... Is the period -during ocillation-from top to bottom back to top? or vice versa. and is the amplitude 1/4 of the period?

Homework Equations

The Attempt at a Solution

 

[americanforest]

Say you have a mass lying on a frictionless table. The mass is attached to a spring which is attached to the wall. The spring is initially unstretched. You stretch it out a certain distance from the initial position. We call that distance d. This is the amplitude of the oscillation. It has units of displacement (distance). Once you then let the spring go from that position, d, it will go back towards its initial, equilibrium position but pass through it and go to position -d on the other side. It will then swing all the way back to position +d, where you initially let it go. The time it takes for it to get back to where you initially let it go is called the period of the motion, T. This quantity has units of time. It depends on the rigidity of the spring and the mass which is attached.

Mathematically, the mass undergoes a motion given by

$$x(t)=d cos(\frac{2 \pi}{T} t)$$

 

[pb23me]

My lab book says x=dsin[2pi/T(t)] ?

 

[americanforest]

It depends on initial conditions. If you start the clock when it is at its biggest displacement (as in my example) then use cosine. This is because the cosine of zero is one. Thus, at time zero, the cosine functions is maximum, just like the distance in my example. That's why I used cosine. If I had started the clock when the mass was moving through the equilibrium position instead of the point of maximum displacement then I would have used sine since the sine of zero is zero.

 

[Liquidxlax]

if your unsure of what AmericanForest means this picture and his explanation together makes a little more sense as you can see that there is a phase shift from cosine to sine

 

[pb23me]

Awsome great clarification! Thanx