Question

$y=(a\sqrt{2} )(\sin\frac{2\pi t}{T} +\cos \frac{2\pi t }{T} )$

Answer 1

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y = a√2(sin 2πt/T + cos 2πt/T) 

we know, sinx + cosx = √2sin(x + π/4) 

so, y = a√2 × √2sin(2πt/T + π/4) 

y = 2a sin(2πt/T + π/4) 

compare this equation with standard equation of simple harmonic motion. 

e.g., y = Asin(2πt/T + \PhiΦ )[/tex]

where A is amplitude, T is time period and \PhiΦ is phase angle. 

hence, amplitude, A = 2a 

time period is T 

and phase angle of wave , \PhiΦ = π/4