Question

ANYBODY PLEASE ANSWER THIS AS SOON AS POSSIBLE....


Show that the function
(sin wt - cos wt) represents simple harmonic motion
​

Answer 1

Answer:

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: