Two SHM-s are represented by x1 - a1 sin - t - -1 and x2 - a2 sin - t - -2- Obtain the expression for the displacement- amplitude and initial phase of the resultant motion-

R= √(a_1^2 + a_2^2 + 2a_1 a_2 cos( α_1 α_2)) ϕ = tan^ 1[ a_1 sinα_1 + a_2 sinα_2a_1 cosα_1 + a_2 cosα_2] ...

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Property 2

Two SHM's are...

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Two SHM's are represented by $x_{1} = a_{1} s i n (ω t + α_{1})$ and $x_{2} = a_{2} s i n (ω t + α_{2})$ . Obtain the expression for the displacement, amplitude and initial phase of the resultant motion.

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X_{1} a sin (ω t + α_{1})

X_{2} a sin (ω t + α_{2})

X_{1} = a_{1} sin ω t

X_{2} = a_{2} sin (ω t + ϕ)

a_{1} = 3.0 c m, a_{2} = 4.0 c m

ϕ

θ^{\circ}

60^{\circ}

90^{\circ}

x_{1} = A_{1} sin ω t

x_{2} = A_{2} sin (ω t + \frac{π}{4})

x_{1} = A_{1} sin ω t

x_{2} = A_{2} sin (ω t + π / 3) .

a_{max}

A,

a_{1}

a_{2}

α_{1}

α_{2}

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