Question

the equation of an shm is x=8sin wt+15coswt where x is displacement and t is time the amplitude will be​

Answer 1

The following equation shows that the particle will be doing an SHM.
Now, let me rearrange the equation by writing that

x = 8 sin wt + 15 sin (90+wt) because cos wt = sin (90+wt)
Which means that both the component shms are in Perpendicular directions to each other.

So, suppose if I now write that
x = 8 sin wt and y = 15 cos wt
This would be absolutely correct
Note*( x = the equation given for resulltant shm where x denotes the net displacement of the trajectory on x-y plane for the particle)
The x and y chosen by me are the axes direction

So,
sin wt = x/8 and cos wt = y/15
Now, by the relation between sin wt and cos wt
I can say that

x^2/64 + y^2/225 = 1

That means, the trajectory of the given particle will be an ellipse.
Now, from the equation of Net amplitude of the particle doing multiple shm

Anet = √A1^2 + A2^2 + 2A1A2 cos theta
where theta is the phase difference between both the component shms

So, here theta = 90°
So,
Anet = √A1^2 + A2^2 = √ (8)^2+(15)^2 = √289 = 17 units.

Hope this helps you !

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