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The position x of a particle moving along x – axis varies with time t as x = Asin ( ωt) where A and ω are positive constants. The acceleration a of particle varies with position x as: a = Ax a = – ω 2 x a = Aωx a = ω 2 xA The position x of a particle moving along x – axis varies with time t as x = Asin (ωt) where A and ω are positive constants. The acceleration a of particle varies with position x as: a = Ax a = – ω2x a = Aωx a = ω2xA
The position x of particle moving along x -axis varies with time as ....(1)x = A sinwt............1differentiate x with respect to time to find velocity of particle at any instant t.e.g., dx/dt = v = wAcoswt we know, acceleration is the rate of change of velocity per unit time.so, differentiate v with respect to time to find Acceleration of particle at any instant t,dv/dt = -w^2Asinwt from equation (1),a = -w^2x
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