Match the parameters given in column I with the expressions given in column II.

Options

A. `1-(ii), 2-(iii), 3-(vi), 4-(i)`
B. `1-(iv), 2-(vi), -(i), 4-(ii)`
C. `1-(vi), 2-(v), 3-(i), 4-(iv)`
D. `1-(i), (2)-(iv), 3-(v), 4-(vi)`

Answer

B

Explanation

`1-(v)`
`sin kt+ cos kt= sqrt(2) sin(kt+(pi)/(4))`
Hence at represents SHM with time period `T=(2pi)/(k)`
`2-(iv) = cos kt+ 2 sin^(2)kx`
`=cos kt+(1-cos^(2)kt)`
`=1+cos kt-cos(2kt)`
This term represents periodic motion. The two terms together have a time period `T=(2pi)/(k)` . The other term 1 is a constant and it is not affected by period.
Hence the motion is not simple harmonic
3 (i) tan kt is not simple harmonic. It is periodic with a period `K=(pi)/(k)`.
4 (iii) `e^(-kt)` decreases to zero as `t to oo`. it is not periodic and hence not simple harmonic. A simple harmonic function must have a period.