A particle is subjected two simple harmonic motions as : x ₁= 7 5 tcm and x₂=2 7 (5 t+ 3 ) cm where x is displacement and t is time in seconds. The maximum acceleration of the particle is x 10⁻² ~ms ⁻² . The value of x is :

Step-by-step solution

aligned & x ₁= 7 5 t & x ₂=2 7 (5 t + 3 ) aligned From phasor, Amplitude of resultant SHM =7 aligned & = ⁻¹ 2 7 3 / 2 7 +2 7 1 2 = ⁻¹ 21 2 7 = ⁻¹ 3 2 & X _ R =7 (5 t + ) & a _ R =-7 25 (5 t + ) & a _ =175 ~cm / sec =175 10⁻² ~m / sec aligned