A particle executes simple harmonic motion represented by displacement function as x ( t ) = A sin ( ω t + ϕ ) . If the position and velocity of the particle at t = 0 s are 2 cm and 2 ω cm s - 1 respe

Question

A particle executes simple harmonic motion represented by displacement function as x ( t ) = A sin ( ω t + ϕ ) . If the position and velocity of the particle at t = 0 s are 2 cm and 2 ω cm s - 1 respectively, then its amplitude is x 2 cm where the value of x is

TestHub · Accepted Answer

x ( t ) = A sin ( ω t + ϕ ) v ( t ) = A ω cos ( ω t + ϕ ) 2 = Asin ϕ . . . 1 2 ω = A ω cos ϕ . . . 2 From ( 1 ) and ( 2 ) tan ϕ = 1 ϕ = 45 ° Putting the value of ϕ in equation ( 1 ) 2 = A 1 2 A = 2 2 x = 2

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