# Simple harmonic motion phase difference problem [duplicate]

Two particles executing SHM of same amplitude of 20cm with same period along the same line about same equilibrium position. The maximum distance between the two is 20cm.

The trouble for me is what should be the equation of position of the SHMs. Is it a sin function or cos function? It seems to me that both the functions should be equivalent because it should not depend upon from where we take the phase of the SHMs. I mean the phase difference between them is constant value.

Please help me visualise the scene going on.

• Draw a picture of 2 SHM systems each consisting of a spring and a block hanging from the ceiling. Since both systems have the same amplitude and period, they're identical. If you pull both blocks down and release them at the same time, they will both execute SHM, they will be in phase, and the maximum distance between them will be 0. And since the systems are identical, draw 1 sin curve and see if you can figure out the phase difference between the 2 systems when one is at an amplitude of 20 cm. and other one at amplitude of 0 cm. – Cinaed Simson Jun 1 '19 at 19:19
• You have answered yourself. Both sin and cos are equivalent. You can use ANY, it does not matter. However, I recommend youu to choose one ands stick to it, it will be easier. But it is your choice. – FGSUZ Jan 31 '20 at 0:49
• Does this answer your question? Which equation to use for simple harmonic motion? – BioPhysicist Jun 3 '20 at 15:10

## 1 Answer

The sin and cos functions are inter convertible .If you start measuring time from the "equilibrium position(displacemen=0)" then you use Sin.

You could use cos if you start time from maximum displacement.

The rule is, if displacement is zero at time zero then use sine.

The Initial phase in SHM depends on the time when we start to calculate the position of particle.

Consider a particle is performing SHM on X-axis and we want to find an equation for it.When we start to measure its x position(t=0),its phase is the initial phase.So if we start to calculate when initial phase is zero (at mean position) we will take sin(wt) which can be converted in cos(wt+π/2) that is a phase difference of π/2.