Question

give the time period for the following periodic motion (W' is any positive constant) 1) sinwt + cos wt 2) sin wt +cos2 wt +sun 4wt.solve..​

Answer 1

Answer:

i-2 pie by Omega

ii 2 pie by omega

Answer 2

question : give the time period for the following periodic motion (w is any positive constant)

1) sinwt + cos wt .

2) sin wt +cos2 wt +sun 4wt .

solution : if a function h(x) = h₁(x) + h₂(x) + h₃(x) + ..... is given where periods of h₁(x) , h₂(x) , h₃(x) .... are T₁, T₂, T₃ ..... respectively.

then, period of h(x) = LCM {T₁, T₂, T₃ .....}

1) sin wt + cos wt

we know, period of sinwt = 2π

period of cos wt = 2π

The period of sinwt + coswt = LCM {2π , 2π} = 2π

2) sinwt + cos2wt + sin4wt

here period of sinwt = 2π

period of cos2wt = 2π/2 = π

period of sin4wt = 2π/4 = π/2

so the period of sinwt + cos2wt + sin4wt = LCM { 2π , π , π/2} = LCM of {2π , π , π}/HCF { 1, 1, 2}

= 2π/1 = 2π

Therefore the period of sinwt + cos2wt + sin4wt is 2π.