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Show that the function
(sin wt - cos wt) represents simple harmonic motion
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According to question, displacement of a particle in one dimension ( say along x-axis) at time t is given by
x(t)=sinwt−coswt
Taking the derivative of x(t) two times with respect to t, you will get the acceleration
d2xdt2=−w2x
This is the differential equation of motion of a a simple harmonic oscillator.
If the particle has mass m whose displacement is given by x(t) , then multiplying above equation by m , we get the force force on the particle as
F=−Kx
where K=mw2
this is a equation of motion of SHM, whose frequency is w.
(In the above answer, I have assumed that you know calculus! )
Explanation:
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