The particle executing simple harmonic motion has a kinetic energy `K_(0)cos^(2) omega t`. The maximum value of potential energy and the total energy are respectively…………and…………..

Options

A. `(K_0)/(2)" and "K_(0)`
B. `(K_0)" and "2K_(0)`
C. `(K_0)" and "K_(0)`
D. `0" and "2K_(0)`

Answer

C

Explanation

Total energy of SHO E= U+K
When kinetic energy x is zero then its potential energy is maximum.
Means `U_("max")+0=E`. Hence `U_("max")= E" ""……."(1)`
Kinetic energy `=(1)/(2) m omega^(2) a^(2) cos^(2) omega t`
`= K_(0) cos^(2) omega t` (is given)
`therefore K_(0)= (1)/(2) m omega^(2) a^(2)=` Total mechanical energy
Now, total mechanical energy `= K_(0)` and maximum potential energy `U_("max")= E= K_(0)`.