Question

2 simple harmonic motions y1=asin wt and y2=acoswt are superimposed on a particle of mass m total mechanical energy of the particles

Answer 1

The total mechanical energy of the particles = ma²w²

The two given harmonic motions y1=a sinwt and y2=a coswt will be superimposed to get a resultant wave -

Y = y1 + y2

Y = a sinwt + a coswt

Y = a sinwt + a sin(90+wt)

Y = a [2sin((2wt +90)/2)cos(90/2)]

Y = a[√2sin(wt + 45)]

Y = √2a sin(wt + 45)

This resultant wave will have an amplitude equal to √2a and the angular velocity will be equal to w .

Mechanical energy = Kinetic Energy + Potential Emergy

=> 1/2 m×(√2a)²× w²

=> ma²w²