Simple Harmonic Motion (displacement function)

[yoohyojinn]

Homework Statement

I learned that in simple harmonic motion,

the displacement fuction is

x(t) = A sin(ωt + Φ)

or

x(t) = A cos(ωt + Φ)

but when do you use sine function or cosine function?

can I use whatever I want whether a sine or cosine function?

And what's that Φ in the equation?

Is it a quantity called a phase angle??

Homework Equations

The Attempt at a Solution

 

[dougla]

Note that cos(x) = sin(x + pi/2)

 

[ehild]

You can use both the sine and cosine functions for the displacement during SHM. You can call Φ phase angle or rather phase constant, and you can determine it form given initial conditions.
If the SHM starts with maximum displacement the cosine function is convenient to use, as x=Acos(ωt) is maximum at t=0, so Φ=0.
In the case when the SHM starts from zero displacement by giving the object some velocity, it is easier to use x=Asin(ωt).

ehild

 

[yeshima]

A boby moves in S.H.M with a amplitude of 30mm and a frequency of 2.0Hz. Calulate the values of
(a) the acceleration at the centre and extremeties.
(b) the velocity at these positions
(c) the velocity and acceleration of a point between the centre and extremity of the oscillation

how would i approach a question like this?...