In a relation F = a sin ( k 1 x ) + b sin ( k 2 T ) where F , x and T denote the force , distance and Time respectively. Units of k 1 and k 2 respectively in S.I units are.
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sin ( k 1 x ) and sin ( k 2 T ) are scalars and without dimensions or units. Since the unit of x is m then that of k 1 is m − 1 , and that of T is s and k 2 is s − 1 . Therefore the answer is m − 1 , s − 1 .
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Angle's are dimensionless quantities.
⇒ k 1 ⋅ x ≡ [ unit of k 1 ] ⋅ m ⇒ [ unit of k 1 ] = m − 1
Similarly
k 2 ⋅ T ≡ [ unit of k 2 ] ⋅ s ⇒ [ unit of k 1 ] = s − 1