Question

In Simple Harmonic Motion, the equation of SHM is x=Acos(ωt+θ) but it is also written as x=Asin(ωt+δ), so what is the relation between two equations? and also what is the relation between the θ and δ?

Answer 1

sin and cos functions are can be interchanged ,depending upon the valpe of theta or delta
eg here you can say delta = theta + pie/2

Answer 2

It is the PHASE of the motion which is affected by using sin or cos.

At angle 0 sin= 0
At angle 0 cos = 1

however if sin(wt+theta) then the phase is 'shifted' by theta

if theta=pi/2 sin (wt+pi/2)= cos(wt)

Answer 3

please write equation of SHM in both sin and cos of angular frequency ω and amplitude A if the particle is situated at \[A/\sqrt{2}\] at t=0 and is going towards mean position?

Answer 4

x = A Sin (wt + θ)
t=0 ,x = A/2^.5 therefore
\[1/\sqrt{2}\] =Sin (θ)
θ = pi/4 or 3pi/4
now dx/dt = A Cos(wt +θ)
at t=0 dx/dt that is velocity is negative (towards mean postion)
so Cosθ is negative therefore θ=3pi/4
x=ASin(wt +3pi/4)
or x = A Cos(wt+ 3pi/4 - pi/2)