Question

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

Answer 1

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 + $\Phi$)[/tex]

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

hence, amplitude, A = 2a

time period is T

and phase angle of wave , $\Phi$ = π/4