Given that the displacement of an oscillating particle, y =A sin(Bx +Ct+D). Find the dimensional formula for (ABCD).

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From the given equation it is clear that (Bx+Ct+D) must be an angle. Therefore (Bx+Ct+D) is a dimensionless quantity because it is an angle. So for that if we want to make this dimension les, B must be in the dimension of (1/x), C must be in the dimension of (1/t) and D should be a number only.Now...
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From the given equation it is clear that (Bx+Ct+D) must be an angle. Therefore (Bx+Ct+D) is a dimensionless quantity because it is an angle. So for that if we want to make this dimension les, B must be in the dimension of (1/x), C must be in the dimension of (1/t) and D should be a number only.Now the left side of the equation is given in the dimension of displacement, so the dimension of A in the right hand must be in the same dimension of 'y'. Therefore it concludes that the dimensions of A,B,C,D are like these, A= [ L M*0 T*0] B=[L*-1 M*0 T*0] C=[L*0 M*0 T*-1] D=[L*0 M*0 T*0] (ABCD)=1/[T] =[M*0 L*0 T*-1] =[T*-1] read less
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